SSC CHSL 2023 PYQ — Question 75

The correct answer is option 3 i.e. $\frac{31}{25}$.

We have a right-angled triangle OPQ, with the right angle at P.

OP = 7 cm

OQ - PQ = 1 cm

⇒ OQ = 1 + PQ

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, OQ² = OP² + PQ²

⇒ (1 + PQ)² = 7² + PQ²

⇒ 1 + 2PQ + PQ² = 49 + PQ²

⇒ 2PQ = 48

⇒ PQ = 24 cm

⇒ OQ = 1 + PQ = 1 + 24 = 25 cm

Now, sin Q = OP/OQ = 7/25

cos Q = PQ/OQ = 24/25

So, sin Q + cos Q = (7/25) + (24/25) = 31/25

Therefore, the value of sin Q + cos Q is 31/25.