SarkariPYQ

SSC CHSL 2025 PYQ — Question 53

SSC CHSL - 12 Nov 2025 - Shift 2 • Quantitative Aptitude • Q53

Back to paper

If cos A = 12/13 and sin B = 5/13, find sin A cos B + cos A sin B:

Show answer & explanation

Correct answer: C

Explanation

sin A cos B + cos A sin B = sin(A + B)
sin²θ + cos²θ = 1
sin A = √(1 − cos²A)
= √(1 − 144/169)
= √(25/169)
= 5/13
cos B = √(1 − sin²B)
= √(1 − 25/169)
= √(144/169)
= 12/13
sin A cos B + cos A sin B=(513×1213)+(1213×513)=120169= \left(\frac{5}{13} \times \frac{12}{13}\right) + \left(\frac{12}{13} \times \frac{5}{13}\right) = \frac{120}{169}