u=\frac{1+\sin\theta}{\cos\theta}\Rightarrowu+\frac{1}{u}=

AP ICET 2017 Shift 1 Paper

Question : 120 of 200

Marks: +1, -0

u={1+\sinθ}/{\cosθ}⇒u+{1}/{u}=

Solution:

u={1+\sinθ}/{\cosθ}

∴\;u+{1}/{u}={1+\sinθ}/{\cosθ}+{\cosθ}/{1+\sinθ}={(1+\sinθ)^{2}+\cos^{2}θ}/{\cosθ(1+\sinθ)}

={1+2\sinθ+\sin^{2}θ+\cos^{2}θ}/{\cosθ(1+\sinθ)}={1+2\sinθ+1}/{\cosθ(1+\sinθ)}

={2(1+\sinθ)}/{\cosθ(1+\sinθ)}={2}/{\cosθ}=2\secθ

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