SSC CGL 2022 PYQ — Question 71

The correct answer is option 2 i.e. -13/85

Given:

sin A = 4/5,

sin B = 15/17

Concept Used:

sin(A - B) = sinAcosB - cosAsinB     ...(i)

$cos\theta = \sqrt{1 - sin^2\theta}$  ...(ii)

Explanation:

Using equation (ii), we get

cosA = $\sqrt{1 - {16\over 25}}$ = 3/5

cosB = $\sqrt{1 - {225 \over 289}}$ = 8/17

Using both the above values in equation (i), we get

⇒ sin(A - B) = ${4\over 5} \times {8 \over 17} - {3 \over 5} \times {15 \over 17}$

⇒ sin(A - B) = $32 - 45 \over 85$ = -13/85.

Hence the value of sin(A - B) is -13/85.