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Question

Evaluate:
3cos557sin354(cos70csc20)7(tan5tan25tan45tan65tan85)

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Solution

We know,
cos(90θ)=sinθ
tan(90θ)=cotθ

cotθ=1tanθ

secθ=1cosθ

cos55=cos(9035)=sin35tan5=tan(9085)=cot85tan25=tan(9065)=cot65csc20=sec(9070)=sec70


Now we will use the above identities to find the value of given expression,

3cos557sin354(cos70csc20)7(tan5tan25tan45tan65tan85)

3sin357sin354(cos70sec70)7(tan5tan25tan45cot25cot5)

374(cos70tan5tan25)7(tan45tan25tan5cos70)

3747

17

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