Question

prove that cos^2-sin^2= 2(cos^2-1) ​

Answer 1

Solution:

To prove: ${ \cos}^{2} \beta - { \sin }^{2} \beta = 2( { \cos }^{2} \beta - 1)$

Taking L.H.S.,

= ${ \cos}^{2} \beta - { \sin }^{2} \beta$

= ${ \cos}^{2} \beta - (1 - { \cos }^{2} \beta)$

= ${ \cos}^{2} \beta - 1 + { \cos }^{2} \beta$

= $2 { \cos}^{2} \beta - 1$ = R.H.S.

Hence Proved

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