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If sin+"cosecx"=2, then what is the val...

If `sin+"cosecx"=2`, then what is the value of `sin^(4)x+"cosec"^(4)x` ?

A

2

B

4

C

8

D

16

Text Solution

Verified by Experts

The correct Answer is:
A
Given `sinx+"cosec"x=2`
Consider `sin^(4)x+"cosec"^(4)x=(sin^(2)x+"cosec"^(2)x)^(2)-2(sin^(2)xcos^(2)x)`
`=[(sinx+"cosec"x)^(2)-)]^(2)-2`
`=(4-2)^(2)-2=2`
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