Question

If ${\sin }^2\theta +\sin \theta =1$, then prove that ${\cos }^2\theta +{\cos }^4\theta =1$.

Answer 1

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

$\sin \theta =1-{\sin }^2\theta$

$\sin \theta ={\cos }^2\theta$

squaring on both sides

${\sin }^2\theta ={\cos }^4\theta$

$\Rightarrow 1-{\cos }^2\theta ={\cos }^4\theta$

$\Rightarrow {\cos }^2\theta +{\cos }^4\theta =1$

Hence it is proved.