Question

Which of the following expressions is equal to 1 – cos4 θ? 1) 2sin2 θ – sin4 θ2) sin2 θ – sin4 θ3) -2sin2 θ – sin4 θ4) 2sin2 θ + sin4 θ

Answer 1

We have to remember that:

`\cos ^2\theta=1-\sin ^2\theta`

Then we have that:

`\begin{gathered} 1-\cos ^4\theta=1-(\cos ^2\theta)^2 \\ =1-(1-\sin ^2\theta)^2 \\ =1-(1-2\sin ^2\theta+\sin ^4\theta) \\ =2\sin ^2\theta-\sin ^4\theta \end{gathered}`

Therefore the answer is 1