Question

prove that 1 + Cos A by sin square A is equal to 1 by 1 - cos squared​

Answer 1

➡$\huge \bf{Question}$

▶Prove that 1 + Cos A by sin square A is equal to 1 by 1 - cos squared.

➡$\huge \bf{Solution}$

SOLVING LEFT HAND SIDE ⤵⤵⤵

$\huge\fbox {L.H.S}$

(1 + CosA) / Sin²A

=> (1 + CosA) / (1 - Cos²A)

[ By the identity :- Sin²A = 1 - Cos²A ]

=> (1 + CosA) / { (1)² - (CosA)² }

=> (1 + CosA) / (1 - CosA)(1 + CosA)

[ By the identity :- (a-b)(a+b) = a² - b² ]

=> 1 / (1 - CosA)

Now , LHS = RHS

$\huge \bf \green{Hence \: Verified} \:$

$\red{For \: more \: explanation \: see \: the \: attachment}$

____________________________

Answer 2

Answer:

1+cosA/sin^2a=1/1-cosa

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$ =1+cosA/sin^2a

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$ =1+cosA/sin^2a =1+cosA /1-cos^2A

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$ =1+cosA/sin^2a =1+cosA /1-cos^2A =1+cosA/(1+cosA)(1-cosA)

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$ =1+cosA/sin^2a =1+cosA /1-cos^2A =1+cosA/(1+cosA)(1-cosA) =1-cosA

1+cosA/sin^2a=1/1-cosaLHS=1+cosA/sin^2a BY USING TRIGONOMETRIC IDENTITY ${ \sin}^{2} a + { \cos }^{2} a = 1$ ${ \sin}^{2} a = 1 - { cosa }^{2}$ =1+cosA/sin^2a =1+cosA /1-cos^2A =1+cosA/(1+cosA)(1-cosA) =1-cosA

Hence proved