Given tan(πcosθ)=cot(πsinθ), then the value of cos(θ−14π) will be-
tan(πcosθ)=cot(πsinθ)=tan[(π2)−πsinθ]∴πcosθ=(π2)−πsinθcosθ+sinθ=(12)cosθ×(1√2)+sinθ×(1√2)=(12√2)cos(θ−(π4))=(12√2)
If sin x=−12, 3π2<x<2π, find the values of sinx2, cosx2 and tan x2.
Or
If tan (π cos θ)=cot (π sin θ), prove that cos(θ−π4)=±12√2.