Question

If $sinx+si{n}^{2}x=1$ then value of $co{s}^{2}x+co{s}^{4}x$ is equal to:

• A. $1$
• B. $2$
• C. $1.5$
• D. none of these

Answer 1

The correct option is A $1$

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

$⟹\sin x=1-{\sin }^{2}x$

$⟹\sin x={\cos }^{2}x$

Squaring on both sides

$⟹{\sin }^{2}x={\cos }^{4}x$

$⟹1-{\cos }^{2}x={\cos }^{4}x$

$⟹{\cos }^{2}x+{\cos }^{4}x=1$