Question

sin⁴theta+cos⁴theta/1+2sin²theta cos²theta=1​

Answer 1

Answer:

Observe that

sin4θ+cos4θ=1−2sin2θcos2θ⟺sin4θ+cos4θ+2sin2θcos2θ=1

which is always true since

sin4θ+cos4θ+2sin2θcos2θ=(sin2θ+cos2θ)2=12=1

so the identity is proved.