Question

Verify:
sin^4x+2sin^2xcos^2x+cos^4x=1

Answer 1

Can you figure out some formula here???

Answer 2

\[\sin^4(x) + \cos^4(x) + 2 \sin^2(x) \cdot \cos^2(x)\]

\[\implies \color{red}{(\sin^2(x))^2 + (\cos^2(x))^2 + 2 \sin^2(x) \cdot \cos^2(x)}\]

Answer 3

Now if you let :

\[\sin^2(x) = a \quad and \; \quad \cos^2(x) = b\] then:

\[\implies a^2 + b^2 + 2ab = (.....)^2 \quad \quad guess ...\]