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Question

The value of sin55osin19o+sin53osin17o is always equal to

A
cos1o2
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B
sin1o
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C
tan1o
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D
cot1o
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Solution

The correct option is A cos1o2
sin55sin19+sin53sin17
=sin55+sin53(sin19+sin17)
2sin(55+53)2cos(55532)=2(sin(19+172))cos(19172)
=2sin54cos12sin18cos1
=2cos1(sin54sin18)
=2cos1(2sin(54182))cos(54+182)
=2cos1sin18cos36
=2cos1(514)(5+14)
=2cos1(416)
=cos12.

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