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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

If cos x +c...

Question

If $cos x + {cos}^{2} x = 1$ , then what is the value of ${sin}^{2} x + {sin}^{4} x$

A

0

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B

1

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C

2

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D

4

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Solution

The correct option is B $1$
$c o s x + c o s^{2} x = 1 \Rightarrow c o s x = 1 - c o s^{2} x = s i n^{2} x$
$\Rightarrow s i n^{2} x + s i n^{4} x = c o s^{x} + c o s^{2} x = 1$

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Similar questions

\frac{{cos}^{4} x}{{cos}^{2} y} + \frac{{sin}^{4} x}{{sin}^{2} y} = 1

\frac{{cos}^{4} y}{{cos}^{2} x} + \frac{{sin}^{4} y}{{sin}^{2} x} = ?

\frac{{cos}^{4} x}{{cos}^{2} y} + \frac{{sin}^{4} x}{{sin}^{2} y} = 1

\frac{{cos}^{4} y}{{cos}^{2} x} + \frac{{sin}^{4} y}{{sin}^{2} x} = 1

cos x

+ {cos}^{2} x = 1

{sin}^{12} x + 3 {sin}^{10} x +

3 {sin}^{8} x + {sin}^{6} x + {sin}^{4} x + 2 {sin}^{2} x - 2

lim x \to \infty \frac{{sin}^{4} x - {sin}^{2} x + 1}{{cos}^{4} x - {cos}^{2} x + 1}

f (x) = \frac{{cos}^{2} x + {sin}^{4} x}{{sin}^{2} x + {cos}^{4} x}

x \in R

f (2018) =

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Standard XII Mathematics

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