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