Question

Prove the following:-
sin^4x + cos^4x+sin^2xcos^2x=( 1-sinxcosx)(1+sinxcosx)​

Answer 1

Step-by-step explanation:

We know that

Sin²x + Cos²x = 1

Doing square both sides

(Sin²x + Cos²x)² = 1

Sin⁴x + Cos⁴x + 2Sin²x*Cos²x = 1

Sin⁴x + Cos⁴x + Sin²x*Cos²x = 1 - Sin²x*Cos²x

Sin⁴x + Cos⁴x + Sin²x * Cos²x

= (1+Sinx*Cosx) (1-Sinx*Cosx)