Question

if
$\sin+ \sin ^{2} = 1$
show that
${ \cos}^{2} + { \cos}^{4} = 1$
​

Answer 1

Given

$\rm{\implies\:sin\theta + sin^2\theta = 1}$$\rm{\implies\:sin\theta = 1 - sin^2\theta}$$\rm{\implies\:sin\theta = cos^2\theta\:\rightarrow(1)}$

Now

$\rm{\implies\: cos^2\theta + \cos^4\theta}$

$\rm{\implies\: cos^2\theta + (\cos^2\theta)^2}$

Using (1)

$\rm{\implies\: cos^2\theta + \sin^2\theta}$

$\rm{\implies\: 1}$