What is the value of tan2 90 ndash theta ndash sin2 90 ndash theta cosec2 90 ndash theta cot2 90 nda...........

Quantitative Aptitude (CGL) Trignometry

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What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?

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Explanation:

Tan2 theta= cot^2(90-θ)
hence , tan^2(90 -θ) = cot 2 θ
therefore LHS (left side) = cosec^2θ-cot^2θ = 1
(by theorem cosec^2θ = 1 + cot^2θa)
cos^2θa= sin^2(90-θ),
hence sin2(90-θ)= cos^2θ,
hence in RHS ,= sin^2θ +sin^2(90-θ)=sin^2θ +cos^2θ= 1
(by theorem sin^2+cos^2 =1)
hence LHS = RHS