{2+\tan ^{2} \\theta+\cot ^{2} \\theta}/{\sec \\theta {\cosec} \\theta} is equal to

Correct Answer is : sec θ cosec θ

SSC CGL 4 06 2019 Shift 1 Paper

Question : 65 of 100

Marks: +1, -0

\ {2+\tan ^{2} \θ+\cot ^{2} \θ}/{\sec \θ\ {\cosec} \θ}

is equal to

Solution:

\ {2+\sec ^{2} \θ-1+\ {\cosec}^{2} \θ-1}/{\sec \θ\.\ {\cosec} \θ}

=\ {\sec ^{2} \θ+\ {\cosec}^{2} \θ}/{\sec \θ\.\ {\cosec} \θ}

=\ {\sec \θ}/{\ {\cosec} \θ}+\ {\ {\cosec} \θ}/{\sec \θ}

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

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

=\sec \θ\.\ {\cosec} \θ

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