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Question

Find the value of: sin(2tan114)+cos(tan122)

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Solution

Given sin(2tan114)+cos(tan122)(1)
sin(2tan114)=sin⎜ ⎜ ⎜ ⎜sin12(14)(14)⎟ ⎟ ⎟ ⎟[2tan1x=sin12x1+x2]
sin(sin12/417/16)
=sin(sin1817)
=817
cos(tan122)
Let tan122=λ
tanλ=22
cosλ=11+tan2λ=11+(22)2=11+8=19
cosλ=13 i.e; cos(tan122)=13
From (1)sin(2tan114)+cos(tan122)
=817+13=24+1751=4151


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