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Question

Prove cos20o+sin20ocos20osin20o=tan65o

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Solution

L.H.S

=cos20+sin20cos20sin20

=sin(9020)+sin20sin(9020)sin20

=sin70+sin20sin70sin20

We know that

sinC+sinD=2sin(C+D2)cos(CD2)

sinCsinD=2cos(C+D2)sin(CD2)

Therefore,

=2sin(70+202)cos(70202)2cos(70+202)sin(70202)

=sin(902)cos(502)cos(902)sin(502)

=sin45cos25cos45sin25

=tan45cot(25)

=1×tan(9065)

=tan65

R.H.S

Hence, proved.


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