If {1}/{ {\cosec} \\theta-1}+ {1}/{ {\cosec} \\theta+1}=2 \sec \\theta, 0^\circ

SSC CGL 7 06 2019 Shift 1 Paper

Question : 62 of 100

Marks: +1, -0

\ \ {1}/{\ {\cosec} \θ-1}+\ {1}/{\ {\cosec} \θ+1}=2 \sec \θ,

0°< \θ <

90°.

then the value of

(\cot \θ+\cos \θ)

is:

Solution:

\ {\sin \θ}/{1-\sin \θ}+\ {\sin \θ}/{1+\sin \θ}=\ {2}/{\cos \θ}

\⇒\ {\sin \θ+\sin ^{2} \θ+\sin \θ-\sin ^{2} \θ}/{1-\sin ^{2} \θ}

=\ {2}/{\cos \θ}

\⇒\ {\sin \θ}{\cos \θ}=1

\⇒\tan \θ=1 ; \θ=45°

Now,

\cot \θ+\cos \θ

\⇒1+\ {1}/{\√{2}} \⇒\ {2+\√{2}}/{2}

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