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Question

If sinθ+cosecθ=2, then the value of sin6θ+cosec6θ is equal to

A
0
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B
1
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C
2
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D
23
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E
26
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Solution

The correct option is C 2
Given that, sinθ+cosecθ=2
Squaring both sides, we get
(sinθ+cosecθ)2=22
sin2θ+cosec2θ+2=4
sin2θ+cosec2θ=2
Cubing both sides, we get
(sin2θ+cosec2θ)3=23
sin6θ+cosec6θ+3sin2θ.cosec2θ(sin2θ+cosec2θ)=8
sin6θ+cosec6θ+6=8
sin6θ+cosec6θ=2
Hence, C is the correct option.

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