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أثبت أن المعادلة الآتية تمثل متطابقة :

secθ(secθcosθ)= tan 2 θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGZb GaaiyzaiaacogacqaH4oqCcaGGOaGaci4CaiaacwgacaGGJbGaeqiU deNaeyOeI0Iaci4yaiaac+gacaGGZbGaeqiUdeNaaiykaiabg2da9i GacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI7aXbaa @4C79@    
secθ(secθcosθ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGZb GaaiyzaiaacogacqaH4oqCcaGGOaGaci4CaiaacwgacaGGJbGaeqiU deNaeyOeI0Iaci4yaiaac+gacaGGZbGaeqiUdeNaaiykaaaa@45F9@                      
 
1 cosθ ( seccosθ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbdaWcaa qaaiaaigdaaeaaciGGJbGaai4BaiaacohacqaH4oqCaaWaaeWaaeaa ciGGZbGaaiyzaiaacogacqGHsislciGGJbGaai4BaiaacohacqaH4o qCaiaawIcacaGLPaaaaaa@4548@ =    
 
cot 2 θ1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGJb Gaai4BaiaacshadaahaaWcbeqaaiaaikdaaaGccqaH4oqCcqGHsisl caaIXaaaaa@3D51@ =    
 
tan 2 θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGG0b Gaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaH4oqCaaa@3BA6@ =    
 
secθ(secθcosθ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGZb GaaiyzaiaacogacqaH4oqCcaGGOaGaci4CaiaacwgacaGGJbGaeqiU deNaeyOeI0Iaci4yaiaac+gacaGGZbGaeqiUdeNaaiykaaaa@45F9@                      
 
1 cosθ ( 1 cosθ cosθ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbdaWcaa qaaiaaigdaaeaaciGGJbGaai4BaiaacohacqaH4oqCaaWaaeWaaeaa daWcaaqaaiaaigdaaeaaciGGJbGaai4BaiaacohacqaH4oqCaaGaey OeI0Iaci4yaiaac+gacaGGZbGaeqiUdehacaGLOaGaayzkaaaaaa@47D3@ =    
 
1 cos 2 θ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIXaaabaGaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGa eqiUdehaaiabgkHiTiaaigdaaaa@3DE5@ =    
 
sec 2 θ1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGZb GaaiyzaiaacogadaahaaWcbeqaaiaaikdaaaGccqaH4oqCcqGHsisl caaIXaaaaa@3D46@ =    
 
tan 2 θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGG0b Gaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaH4oqCaaa@3BA6@ =    
 
secθ(secθcosθ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGGZb GaaiyzaiaacogacqaH4oqCcaGGOaGaci4CaiaacwgacaGGJbGaeqiU deNaeyOeI0Iaci4yaiaac+gacaGGZbGaeqiUdeNaaiykaaaa@45F9@                      
 
1 sinθ ( 1 sinθ cosθ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbdaWcaa qaaiaaigdaaeaaciGGZbGaaiyAaiaac6gacqaH4oqCaaWaaeWaaeaa daWcaaqaaiaaigdaaeaaciGGZbGaaiyAaiaac6gacqaH4oqCaaGaey OeI0Iaci4yaiaac+gacaGGZbGaeqiUdehacaGLOaGaayzkaaaaaa@47DD@ =    
 
1 sin 2 θ cosθ sinθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbdaWcaa qaaiaaigdaaeaaciGGZbGaaiyAaiaac6gadaahaaWcbeqaaiaaikda aaGccqaH4oqCaaGaeyOeI0YaaSaaaeaaciGGJbGaai4Baiaacohacq aH4oqCaeaaciGGZbGaaiyAaiaac6gacqaH4oqCaaaaaa@468C@ =    
 
cos 2 θ sin 2 θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbdaWcaa qaaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiabeI7a XbqaaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiabeI 7aXbaaaaa@4139@ =    
 
tan 2 θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWYbciGG0b Gaaiyyaiaac6gadaahaaWcbeqaaiaaikdaaaGccqaH4oqCaaa@3BA6@ =    
 
            
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