The value of \\sqrt{\sec ^{2} \\theta+ {\cosec}^{2} \\theta} \times \\sqrt{\tan ^{2} \\theta-\sin ^{2} \\theta} isequal to:

Correct Answer is : sinθsec2θ

{\cosec} \\theta\sec ^{2} \\theta

{\cosec} \\theta\cos ^{2} \\theta

SSC CGL 6 06 2019 Shift 2 Paper

Question : 71 of 100

Marks: +1, -0

The value of

\√{\sec ^{2} \θ+\ {\cosec}^{2} \θ} \

× \√{\tan ^{2} \θ-\sin ^{2} \θ}

isequal to:

Solution:

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

× \√{\ {\sin ^{2} \θ}/{\cos ^{2} \θ}-\sin ^{2} \θ}

=\ {1}/{\sin \θ \.\cos \θ} \

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

=\ {1}/{\sin \θ\.\cos \θ} \× \ {\sin \θ\.\sin \θ}/{\cos \θ}

=\sin \θ\.\sec ^{2} \θ

Go to Question:

Prev Question

Next Question