SarkariPYQ

SSC CHSL 2023 PYQ — Question 62

SSC CHSL - 09 March 2023 - Shift 2 • Quantitative Aptitude • Q62

Back to paper

What is the value of tanA−sinAtanA+sinA\frac{tanA - sinA}{tanA+sinA}?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. secA−1secA+1\frac{sec A-1}{sec A + 1}.

tanA−sinAtanA+sinA\frac{tanA - sinA}{tanA+sinA}

=sin⁡Acos⁡A−sin⁡Asin⁡Acos⁡A+sin⁡A=\frac{\frac{\sin A}{\cos A} - \sin A}{\frac{\sin A}{\cos A} + \sin A}

=sin⁡A(1cos⁡A−1)sin⁡A(1cos⁡A+1)=\frac{\sin A \left( \frac{1}{\cos A} - 1 \right)}{\sin A \left( \frac{1}{\cos A} + 1 \right)}

=1cos⁡A−11cos⁡A+1=\frac{\frac{1}{\cos A} - 1}{\frac{1}{\cos A} + 1}

=sec⁡A−1sec⁡A+1=\frac{\sec A - 1}{\sec A + 1}