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Trigonometric Equations

If sin x+sin ...

Question

If $s i n x + s i n^{2} x = 1$ , then write the value of $c o s^{8} x + 2 c o s^{6} x + c o s^{4} x .$

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Solution

$s i n x + s i n^{2} x = 1$

$s i n x = 1 - s i n^{2} x = c o s^{2} x$

$c o s^{8} x + 2 c o s^{6} x + c o s^{4} x$

$= s i n^{4} x + 2 s i n^{3} x + s i n^{2} x$

$= (s i n x + s i n^{2} x)^{2}$

=1

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Similar questions

sin x + {sin}^{2} x = 1

then the value of

{cos}^{8} x + 2 {cos}^{6} x + {cos}^{4} x

S i n x + S i n^{2} x = 1

C o s^{8} x + 2 C o s^{6} x + C o s^{4} x = . . . . . . .

s i n x + s i n^{2} x = 1

, then the value of

c o s^{2} x + c o s^{4} x

s i n x + s i n^{2} x = 1

c o s^{2} x + c o s^{4} x

sin x + {sin}^{2} x = 1

then prove that

{cos}^{2} x + {cos}^{4} x = 1

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