TS ICET 2017 Question Paper with Solutions for online practice

Question : 119 of 200

Marks: +1, -0

If cot θ + cosec θ = p ≠ 0. then cos θ =

Solution:

\cosθ=\cos^{2}{θ}/{2}-\sin^{2}{θ}/{2}

.....(i)
Given :

\cotθ+\cosecθ=p

⇒{\cosθ}/{\sinθ}+{1}/{\sinθ}=p⇒{\cosθ+1}/{\sinθ}=p

⇒{2\cos^{2}{θ}/{2}}/{2\sin{θ}/{2}⋅\cos{θ}/{2}}=p⇒{\cos{θ}/{2}}/{\sin{θ}/{2}}=p

.....(ii)

p^{2}-1={\cos^{2}{θ}/{2}-\sin^{2}{θ}/{2}}/{\sin^{2}{θ}/{2}}

p^2+1={\cos^2θ/2+\sin^2θ/2}/{\sin^2θ/2}=1/{\sin^2θ/2}

∴{p^{2}-1}/{p^2+1}=\cos^{2}{θ}/{2}-\sin^{2}{θ}/{2}=\cosθ

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