Question

If sin x + cosec x = 2, then write the value of sinⁿ x + cosecⁿ x.

 

Answer 1

We have: 
\[\sin x + cosec x = 2\]
\[ \Rightarrow \sin x + \frac{1}{\sin x} = 2\]
\[ \Rightarrow \frac{\sin^2 x + 1}{\sin x} = 2\]
`=>sin^2x+1=2sinx`

`=>sin^2x+1-2sinx=0`

`=>(sinx-1)^2=0`

`=>sinx-1=0`

`=>sinx=1`

And `cosec x=1/(sinx)=1`

`thereforesin^nx+cosec^nx=1^n+1^n`

= 1 + 1 = 2