Question

If $\cos A+{\cos }^{2}A=1$ then the value of ${\sin }^{2}A+{\sin }^{4}A$ is

• A. $0$
• B. $-1$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$1$

As given

$cosA+co{s}^{2}A=1$

$\Rightarrow cosA=1-co{s}^{2}A$

$\because 1-co{s}^{2}A=si{n}^{2}A$

$\therefore cosA=si{n}^{2}A$......1

Then $si{n}^{2}A+si{n}^{4}A$

$\Rightarrow si{n}^{2}A+(si{n}^{2}A{)}^2$

From 1

$\Rightarrow cosA+co{s}^{2}A\Rightarrow 1$