What is the simplified value of (\frac{\sec A}{\cot A + \tan A})^2 ?

SSC CGL 8 Aug 2017 Shift 1 Paper

Question : 70 of 100

Marks: +1, -0

What is the simplified value of

({\sec A}/{\cot A + \tan A})^2

Solution:

({\sec A}/{\cot A + \tan A})^2

=[{1/\cosA}/{\cosA/\sinA+\sinA/\cosA}]^2

=[1/\cosA× {\sinA \cosA}/{\cos^2A +\sin^2A}]^2

=[\sinA/1]^2=\sin^2A=1-\cos^2A

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