{ 1 + \cos \\theta + \sin \\theta } /{ 1 - \cos \\theta + \sin \\theta }

TS ICET 2017 Question Paper with Solutions for online practice

Question : 120 of 200

Marks: +1, -0

{ 1 + \cos \θ + \sin \θ } /{ 1 - \cos \θ + \sin \θ }

Solution:

{1+\cos\θ+\sin\θ}/{1-\cos\θ+\sin\θ}

=\;\;{2\cos^{2}\;\;{θ}/{2}+2\sin\;\;{θ}/{2}\cos\;\;{θ}/{2}}/{2\sin^{2}\;\;{θ}/{2}+2\sin\;\;{θ}/{2}\cos\;\;{θ}/{2}}

\;\;{2\cos\;\;{θ}/{2}(\cos\;\;{θ}/{2}+\sin\;\;{θ}/{2})}/{2\sin\;\;{θ}/{2}(\sin\;\;{θ}/{2}+\cos\;\;{θ}/{2})}=\;\;{\cos\;\;{θ}/{2}}/{\sin\;\;{θ}/{2}}=\cot\;\;{θ}/{2}

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