Question

If sin x + cosec X = 2, then find the value of sin^10 x + cosec^10x.​

Answer 1

Answer:

1024 is the answer.

We have to find the value of 2 power 10

Answer 2

Answer:

${ \sin(x) }^{10} + { \csc(x) }^{10} = 2$

Explanation :-

Given,

$\sin(x) + \csc(x) = 2 \\ \\ \implies \sin(x) + \frac{1}{ \sin(x) } = 2$

This is only possible when $\sin(x)\:=\:1\:or\:-1$

Therefore,

${ \sin(x) }^{10} + { \csc(x) }^{10} \\ \\ = { \sin(x) }^{10} + \frac{1}{{ \sin(x) }^{10} } \\ \\ = {1}^{10} + \frac{1}{ {1}^{10} } = 2$

Important concept

Whenever we come across such equations where $x^2\:+\:\dfrac{1}{x^2}\:=\:2$ ,There is only when possible case where x = 1 or x = -1.