SarkariPYQ

SSC CGL 2024 PYQ — Question 57

SSC CGL - 09 Sep 2024 - Shift 3 • Quantitative Aptitude • Q57

Back to paper

If A is an acute angle, which of the following is equal to sin A1 + cos Asin\ A \over 1\ +\ cos\ A?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1−cosAsinA1-cosA\over sinA.

We know that,

⇒ sin2A + cos2A = 1

Now,

⇒ sin A1 + cos Asin\ A \over 1\ +\ cos\ A × 1−cosA1 − cos A1 - cosA \over 1\ -\ cos\ A

⇒ sin A(1−cosA)12 − cos2 Asin\ A(1-cosA) \over 1^2\ -\ cos^2\ A

⇒ sin A(1−cosA)sin2Asin\ A(1-cosA) \over sin^2A = 1−cosAsinA1-cosA\over sinA