Question

help with this please​

Answer 1

$\texttt{Trigonometric identity}$

$\boxed{\sin^{2}\theta+\cos^{2}\theta=1}$

So, we get

$\sin^{4}\theta=(1-\cos^{2}\theta)^{2}$

Substitute to replace in terms of $\cos\theta$.

$\text{L.H.S}$

$=(1-2\cos^{2}\theta+\cos^{2}\theta)+\cos^{2}\theta$

$=1-2\cos^{2}\theta+2\cos^{2}\theta$

$=\text{R.H.S}$

Hence, it is proved.