Question

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

Answer 1

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

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

$\sin \theta ={\cos }^2\theta$............(i)

To find value of ${\cos }^2\theta +{\cos }^4\theta$

${\cos }^2\theta +({\cos }^2\theta {)}^2=\sin \theta +(\sin \theta {)}^2$.........from (i)

$=\sin \theta +\sin \theta$

$=1$ ($\therefore$ It is given $\sin \theta +{\sin }^2\theta =1$)