If tan(πcosθ)=cot(πsinθ) then find the value of cos(θ−π4).
I could not get any idea to solve. However I tried by using θ=0∘. But could not get the answer.
Answer
Hint -
tan(πcosθ)=cot(πsinθ)
tan(πcosθ)=tan(π2−πsinθ)
πcosθ=π2−πsinθ
cosθ=12−sinθ
sinθ+cosθ=12
Now we have,
cos(θ−π4)
=cosθcosπ4+sinθsinπ4
=cosθ1√2+sinθ1√2
=1√2(cosθ+sinθ)
=1√2(12)
=12√2
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