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Question

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


Solution

Let y=sin(2tan114)+cos(tan122)=u+v, where u=sin2 tan114 and v=cos tan122
u=sin(2tan114)=sin sin1[2.141+(14)2]=241716=817
Also, v=cos tan122[Put  tan122=θ  tan θ=22cos θ=13 θ=cos113
v=cos(cos113)=13
Now, y=u+v=817+13=4151.

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