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Trigonometric Equations

If sin x+cose...

Question

If sin x +cosec x =2, then write the value of $s i n^{n} x + c o s e c^{n} x .$

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Solution

sin x +cosec x =2

$s i n x + \frac{1}{s i n x} = 2$

1+sin x=2 sin x

sin x =1

cosec x =1

$s i n^{n} x + c o s e c^{n} x = (s i n x)^{n} + (c o s e c x)^{n}$

=1+1 =2

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