\sqrt{ \frac{1+\sin \\theta}{1-\sin \\theta}}+\sqrt{ \frac{1-\sin \\theta}{1+\sin \\theta}} is equal to

SSC CPO SI and ASI 2014 Paper

Question : 142 of 200

Marks: +1, -0

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

is equal to

Solution:

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

= √{ ({1+\sin \θ})^2/{1-\sin^2 \θ}}+√{ ({1-\sin \θ})^2/{1-\sin^2\θ}}

( by rationalisation)

= √{ ({1+\sin \θ})^2/{ \cos^2 \θ}}+√{ ({1-\sin \θ})^2/{ \cos^2 \θ}}

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

= {2}{\cos \θ}=2 \sec \θ

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