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Question

The value of cos1(12(cos7π5sin2π5)) is

A
23π20
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B
13π20
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C
3π20
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D
17π20
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Solution

The correct option is D 17π20
12(cos7π5sin2π5)=cosπ4cos7π5sinπ4sin2π5=cosπ4cos7π5+sinπ4sin7π5
=cos(7π5π4)=cos(23π20)=cos(π+3π20)=cos(3π20)

cos1{12(cos7π5sin2π5)}=cos1(cos(3π20))=π3π20=17π20
(since 17π20 lies between 0 and π)

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