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Antiderivative

If cos x + ...

Question

If cos x + $c o s^{2} x$ = 1, then what is the value of $s i n^{2} x + s i n^{4} x$ ?

A

0

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B

1

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C

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D

4

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Solution

The correct option is B 1
Given that, cos x + $c o s^{2}$ x =1
cos x = 1 - $c o s^{2} x = s i n^{2} x$
$s i n^{2}$ x = cos x
On squaring, we get
$s i n^{4} x = c o s^{2} x a n d s i n^{2} x$ = cos x
Hence, $s i n^{2} x + s i n^{4} x = c o s . x + c o s^{2} x = 1$

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