If + ^2A=1, then ^2A+ ^4A= - Vidyadip

MCQ

If $\cos\text{A}+\cos^2\text{A}=1,$ then $\sin^2\text{A}+\sin^4\text{A}=$

A
$-1$
B
$0$
✓
$1$
D
None of these.

✓

Answer

Correct option: C.

$1$

Given,
$\cos\text{A}+\cos^2\text{A}=1$
$\Rightarrow\ 1-\cos^2\text{A}=\cos\text{A}$
So $, \sin^2\text{A}+\sin^4\text{A}$
$=\sin^2\text{A}+\sin^2\text{A}\sin^2\text{A}$
$=\sin^2\text{A}+(1-\cos^2\text{A})(1-\cos^2\text{A})$
$=\sin^2\text{A}+\cos\text{A}\cos\text{A}$
$=\sin^2\text{A}+\cos^2\text{A}$
$=1$
Hence, the correct option is $(c).$

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