Question

If sin x+ sin^2x=1 then show that cos^2x + cos^4x=1

Answer 1

Answer:

Hence proved $cos^{2}x+cos^{4} x=1$.

Step-by-step explanation:

It is given that $sin\ x+sin^{2}x=1$.

Then, $sin\ x=1-sin^{2}x=cos^{2}x$

Compute the value of $cos^{2}x+cos^{4} x$ as follows:

$cos^{2}x+cos^{4} x=cos^{2}x+(cos^{2} x)^{2}$

                      $=sin\ x+(sin\ x)^{2}$

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

Hence proved $cos^{2}x+cos^{4} x=1$.