Question

sin⁴α+cos⁴α+2sin²α.cos²α

Answer 1

\(\left(sin^2\alpha\right)^2+\left(cos^2\alpha\right)^2+2.sin\alpha.cos\alpha\\ =\left(sin^2\alpha+cos^2\alpha\right)^2\\ =\left(1\right)^2=1\)

Answer 2

\(\sin^4\alpha+2\cdot\sin^2\alpha\cdot\cos^2\alpha+\cos^4\alpha\)

\(=\left(\sin^2\alpha+\cos^2\alpha\right)^2\)

=1