SarkariPYQ

SSC CGL 2022 PYQ — Question 55

SSC CGL - 03 Dec 2022 - Shift 1 • Quantitative Aptitude • Q55

Back to paper

Simplify : cosA1+tanA−sinA1+cotA{{cosA} \over 1+tanA}-{{sinA} \over 1+cotA}.

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. cosA - sinA.

Formula used:

a2 - b2 = (a - b)(a + b)

Calculations:

⇒ cos A/(1 + sin A/cos A) - sin A/(1 + cos A/sin A)

⇒ cos2A/(cos A + sin A) - sin2A/(cos A + sin A)

⇒ (cos2A - sin2A)/(cos A + sin A)

⇒ (cos A + sin A)(cos A - sin A)/(cos A + sin A)

⇒ cos A - sin A