What is the simplified value of [(\tan^2 \\theta-\sin^2 \\theta)/{ \tan^2 \\theta\sin^2 \\theta}] ?

SSC CGL 11 Aug 2017 Shift 1 Paper

Question : 69 of 100

Marks: +1, -0

What is the simplified value of

[(\tan^2 \θ-\sin^2 \θ)/{ \tan^2 \θ\sin^2 \θ}]

Solution:

{\tan^2 \θ-\sin^2 \θ}/{ \tan^2 .\θ\sin^2 \θ} =1/{\sin^2θ}-1/{\tan^2θ}

=1/{\sin^2θ}- {\cos^2θ}/{\sin^2θ}

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

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