Question

cosec-sin=m and sec - cos= n show (m²n)⅔- (mn²)⅔ =1

Answer 1

Explanation:

m2n=(cosecθ−sinθ)2(secθ−cosθ)=(sinθ1−sin2θ)2(cosθ1−cos2θ)=sin2θcosθcos4θsin2θ

⇒(m2n)=cos3θ

⇒(m2n)2/3=cos2θ

Similarly mn2=(cosecθ−sinθ)(secθ−cosθ)2=cos2θsinθsin4θcos2θ=sin3θ

⇒(m2n)2/3+(mn2)2/3=sin2θ+cos2θ=1.

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