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أثبت أن المعادلة الآتية تمثل متطابقة :

cosθ(1+ tan 2 θ) cscθ =tanθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcaGGOaGaaGymaiabgUcaRiGacsha caGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI7aXjaacMcaae aaciGGJbGaai4CaiaacogacqaH4oqCaaGaeyypa0JaciiDaiaacgga caGGUbGaeqiUdehaaa@4D09@    
cosθ(1+ tan 2 θ) cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcaGGOaGaaGymaiabgUcaRiGacsha caGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI7aXjaacMcaae aaciGGJbGaai4CaiaacogacqaH4oqCaaaaaa@477C@                      
 
cosθ sin 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHIaYTciGGZbGaaiyAaiaac6ga daahaaWcbeqaaiaaikdaaaGccqaH4oqCaeaaciGGJbGaai4Caiaaco gacqaH4oqCaaaaaa@4612@ =    
 
cosθ(1 cos 2 θ) cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHIaYTcaGGOaGaaGymaiabgkHi TiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeI7aXj aacMcaaeaaciGGJbGaai4CaiaacogacqaH4oqCaaaaaa@490E@ =    
 
sinθ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGZbGaaiyzaiaacogacqaH4oqCaeaaciGGJbGaai4CaiaacogacqaH 4oqCaaaaaa@3F02@ =    
 
1 cscθ 1 sinθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada WcaaqaaiaaigdaaeaaciGGJbGaai4CaiaacogacqaH4oqCaaaabaWa aSaaaeaacaaIXaaabaGaci4CaiaacMgacaGGUbGaeqiUdehaaaaaaa a@40A7@ =    
 
sinθ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGZbGaaiyAaiaac6gacqaH4oqCaeaaciGGJbGaai4BaiaacohacqaH 4oqCaaaaaa@3F1D@ =    
 
tanθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaeqiUdehaaa@3A7D@ =    
 
cosθ(1+ tan 2 θ) cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcaGGOaGaaGymaiabgUcaRiGacsha caGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI7aXjaacMcaae aaciGGJbGaai4CaiaacogacqaH4oqCaaaaaa@477C@                      
 
cosθ+cosθ tan 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHRaWkciGGJbGaai4Baiaacoha cqaH4oqCciGG0bGaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaaGccq aH4oqCaeaaciGGJbGaai4CaiaacogacqaH4oqCaaaaaa@49F1@ =    
 
cosθ+cosθ sin 2 θ cos 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHRaWkciGGJbGaai4Baiaacoha cqaH4oqCcqGHIaYTdaWcaaqaaiGacohacaGGPbGaaiOBamaaCaaale qabaGaaGOmaaaakiabeI7aXbqaaiGacogacaGGVbGaai4CamaaCaaa leqabaGaaGOmaaaakiabeI7aXbaaaeaaciGGJbGaai4Caiaacogacq aH4oqCaaaaaa@5109@ =    
 
cosθ+ sin 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHRaWkciGGZbGaaiyAaiaac6ga daahaaWcbeqaaiaaikdaaaGccqaH4oqCaeaaciGGJbGaai4Caiaaco gacqaH4oqCaaaaaa@456F@ =    
 
1 cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaci4yaiaacohacaGGJbGaeqiUdehaaaaa@3B3E@ =    
 
tanθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaeqiUdehaaa@3A7D@ =    
 
cosθ(1+ tan 2 θ) cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcaGGOaGaaGymaiabgUcaRiGacsha caGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI7aXjaacMcaae aaciGGJbGaai4CaiaacogacqaH4oqCaaaaaa@477C@                      
 
cosθ sec 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGJbGaai4BaiaacohacqaH4oqCcqGHIaYTciGGZbGaaiyzaiaacoga daahaaWcbeqaaiaaikdaaaGccqaH4oqCaeaaciGGJbGaai4Caiaaco gacqaH4oqCaaaaaa@4603@ =    
 
1 secθ sec 2 θ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada WcaaqaaiaaigdaaeaaciGGZbGaaiyzaiaacogacqaH4oqCaaGaeyOi GCRaci4CaiaacwgacaGGJbWaaWbaaSqabeaacaaIYaaaaOGaeqiUde habaGaci4yaiaacohacaGGJbGaeqiUdehaaaaa@46C4@ =    
 
secθ cscθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGZbGaaiyzaiaacogacqaH4oqCaeaaciGGJbGaai4CaiaacogacqaH 4oqCaaaaaa@3F02@ =    
 
1 cosθ 1 sinθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada WcaaqaaiaaigdaaeaaciGGJbGaai4BaiaacohacqaH4oqCaaaabaWa aSaaaeaacaaIXaaabaGaci4CaiaacMgacaGGUbGaeqiUdehaaaaaaa a@40B3@ =    
 
sinθ cosθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci GGZbGaaiyAaiaac6gacqaH4oqCaeaaciGGJbGaai4BaiaacohacqaH 4oqCaaaaaa@3F1D@ =    
 
tanθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacg gacaGGUbGaeqiUdehaaa@3A7D@ =    
 
            
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