Question

(cos⁴θ − sin⁴θ)=?
(a) 1 − 2 sin²θ
(b) 1 − 2 cos²θ
(c) 2 − sin²θ
(d) 2 − cos²θ

Answer 1

a) 1 − 2 sin²θ

$$\begin{gathered} ({\text{cos}}^4\theta -{\text{sin}}^4\theta ) \\ ={\left({\text{cos}}^2\theta \right)}^2-{\left({\text{sin}}^2\theta \right)}^2 \\ =({\text{cos}}^2\theta +{\text{sin}}^2\theta )({\text{cos}}^2\theta -{\text{sin}}^2\theta ) \\ =1(1-{\text{sin}}^2\theta -{\text{sin}}^2\theta ) \\ =1-2{\text{sin}}^2\theta \end{gathered}$$