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أثبت أن المعادلة الآتية متطابقة  :     tan2θ= 2 cotθtanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacggacaGGUbGaaGOmaGGaciab=H7aXjabg2da9maalaaabaGaaGOmaaqaaiGacogacaGGVbGaaiiDaiab=H7aXjabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@46B5@          
tan2θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacggacaGGUbGaaGOmaGGaciab=H7aXjabg2da9maalaaabaGaaGOmaaqaaiGacogacaGGVbGaaiiDaiab=H7aXjabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@46B5@                        
 
2tanθ 1 tan 2 θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaGaciiDaiaacggacaGGUbacciGae8hUdehabaGaaGymaiabgkHiTiGacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiab=H7aXbaaaaa@421C@ =      
 
2· tanθ tanθ 1 tanθ tan 2 θ tanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaGaeS4JPF2aaSaaaeaaciGG0bGaaiyyaiaac6gaiiGacqWF4oqCaeaaciGG0bGaaiyyaiaac6gacqWF4oqCaaaabaWaaSaaaeaacaaIXaaabaGaciiDaiaacggacaGGUbGae8hUdehaaiabgkHiTmaalaaabaGaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGae8hUdehabaGaciiDaiaacggacaGGUbGae8hUdehaaaaaaaa@5242@ =      
 
1 tanθ tanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaWaaSaaaeaacaaIXaaabaGaciiDaiaacggacaGGUbacciGae8hUdehaaiabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@4139@ =      
 
2 cotθtanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaGaci4yaiaac+gacaGG0bacciGae8hUdeNaeyOeI0IaciiDaiaacggacaGGUbGae8hUdehaaaaa@4071@ =      
 
tan2θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacggacaGGUbGaaGOmaGGaciab=H7aXjabg2da9maalaaabaGaaGOmaaqaaiGacogacaGGVbGaaiiDaiab=H7aXjabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@46B5@                        
 
2tanθ 1 tan 2 θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaGaciiDaiaacggacaGGUbacciGae8hUdehabaGaaGymaiabgkHiTiGacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiab=H7aXbaaaaa@421C@ =      
 
2 tanθ tan 2 θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaGaciiDaiaacggacaGGUbacciGae8hUdeNaeyOeI0IaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGae8hUdehaaaaa@4161@ =      
 
2 1 tanθ tanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaWaaSaaaeaacaaIXaaabaGaciiDaiaacggacaGGUbacciGae8hUdehaaiabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@4139@ =      
 
2 cotθtanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaGaci4yaiaac+gacaGG0bacciGae8hUdeNaeyOeI0IaciiDaiaacggacaGGUbGae8hUdehaaaaa@4071@ =      
 
tan2θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiDaiaacggacaGGUbGaaGOmaGGaciab=H7aXjabg2da9maalaaabaGaaGOmaaqaaiGacogacaGGVbGaaiiDaiab=H7aXjabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@46B5@                        
 
2tanθ 1 tan 2 θ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaGaciiDaiaacggacaGGUbacciGae8hUdehabaGaaGymaiabgkHiTiGacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiab=H7aXbaaaaa@421C@ =      
 
2· tanθ tanθ 1 tanθ tan 2 θ tanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaGaeS4JPF2aaSaaaeaaciGG0bGaaiyyaiaac6gaiiGacqWF4oqCaeaaciGG0bGaaiyyaiaac6gacqWF4oqCaaaabaWaaSaaaeaacaaIXaaabaGaciiDaiaacggacaGGUbGae8hUdehaaiabgkHiTmaalaaabaGaciiDaiaacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGae8hUdehabaGaciiDaiaacggacaGGUbGae8hUdehaaaaaaaa@5242@ =      
 
2 1 tanθ tanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaWaaSaaaeaacaaIXaaabaGaciiDaiaacggacaGGUbacciGae8hUdehaaiabgkHiTiGacshacaGGHbGaaiOBaiab=H7aXbaaaaa@4139@ =      
 
2 cotθtanθ MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIYaaabaGaci4yaiaac+gacaGG0bacciGae8hUdeNaeyOeI0IaciiDaiaacggacaGGUbGae8hUdehaaaaa@4071@ =      
 
            
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