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

AP ICET 2019 Shift 2 Paper

Question : 118 of 200

Marks: +1, -0

{1+\sinθ}/{\cosθ}+ {\cosθ}/{1+\sinθ}

Solution:

Let

u={1+\sin θ}/{\cos θ}

={1}/{\cos θ}+\;{\sin θ}/{\cos θ}

=\sec θ+\tan θ

∴{1}/{u}={1}/{\sec θ+\tan θ}=\sec θ-\tan θ

u+{1}/{u}=\sec θ+\tan θ+\sec θ-\tan θ

=2 \sec θ

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