Question

sin to the power 4 A minus Cos to the power 4 A equals to 2 sin square A minus one

Answer 1

Hope this helps you ☺☺

Answer 2

HENCE PROVED.

$\rightarrow \: {\sin}^{4} (A) - { \cos}^{4} (A) = 2 { \sin }^{2} (A) - 1$

Step-by-step explanation:

Given:We have to prove

$\rightarrow \: {\sin}^{4} (A) - { \cos}^{4} (A) = 2 { \sin }^{2} (A) - 1$

Taking LHS,

$\rightarrow \: { \sin }^{4} (A) - { \cos }^{4} (A) \\ \rightarrow \: ({ \sin }^{2} (A) - { \cos }^{2} (A)) \times ( \: { \sin }^{2} (A) + { \cos }^{2} (A)) \\ \rightarrow \: ({ \sin }^{2} (A) - { \cos }^{2} (A)) \\ \rightarrow \: ({ \sin }^{2} (A) - (1 - { \sin }^{2} (A))) \\ \rightarrow \: 2{ \sin }^{2} (A) - 1$

Hence, LHS=RHS.