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Question

The value of sin1(sin(17π4))+cos1(cos(27π5))+tan1(tan(37π6)) is

A
50π51
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B
61π60
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C
71π70
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D
41π40
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Solution

The correct option is B 61π60
Let y=sin1(sin(17π4))+cos1(cos(27π5))+tan1(tan(37π6))
Now, sin(17π4)=sin(4π+π4)=sinπ4 and
cos(27π5)=cos(6π3π5)=cos3π5 and
tan(37π6)=tan(6π+π6)=tanπ6

y=sin1sinπ4+cos1cos3π5+tan1tanπ6
y=π4+3π5+π6=61π60

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