Evaluating \frac{\cos 81^{\circ}}{\sin 3^{\circ} \sin 57^{\circ} \sin 63^{\circ}}

Swebaceacichegh

Swebaceacichegh

Answered question

2022-01-26

Evaluating cos81sin3sin57sin63

Answer & Explanation

sphwngzt

sphwngzt

Beginner2022-01-27Added 11 answers

Let α=60  and  θ=3. The numerator is
cos81=sin9=sin3θ
=sinθcos2θ+cosθsin2θ
=sinθ(cos2θ+2cos2θ)
=sinθ(2cos2θ+1)
while the denominator equals to
sin3sin57sin63=sinθsin(αθ)sin(α+θ)
=12sinθ(cos2θcos2α)
=14sinθ(2cos2θ+1)
This means the expression at hand equals to 4.

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