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Question

The value of sec[sin1(sin50π9)+cos1cos(31π9)] is equal to

A
sec10π9
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B
secπ9
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C
1
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D
1
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Solution

The correct option is D 1
sec[sin1(sin(50π9))+cos1(cos(31π9))]
=sec[sin1(sin(50π9))+cos1(cos(31π9))]
=sec[sin1(sin(6π4π9))+cos1(cos(3π+4π9))]
=sec[sin1(sin(4π9))+cos1(cos(4π9))]
=sec[sin1(sin(4π9))+πcos1(cos(4π9))]
=sec[4π94π9+π]
=sec[π]
=1

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