SSC CGL 2025 Tier-I · 19 September 2025, Shift 1 · Quantitative Aptitude · Question 15 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What is the value of sin 20° cos 10° + cos 20° sin 10°?

(a)1⁄2
(b)3⁄4
(c)5⁄4
(d)7⁄8

Answer

Why

Correct — A.
The pattern sinA cosB + cosA sinB is the expansion of sin(A + B).
Here A = 20° and B = 10°: sin(20° + 10°) = sin 30°
sin 30° = 1⁄2 → option (a).

Why the others are wrong

(b)
3⁄4 — 3⁄4 is (√3⁄2)², the square of cos 30°. The formula collapses to a plain sine, sin 30° = 1⁄2, with no squaring anywhere.
(c)
5⁄4 — 5⁄4 is greater than 1, and a sine never exceeds 1. The expression equals sin 30°, so it cannot be 5⁄4.
(d)
7⁄8 — 7⁄8 = 0.875 fails a numerical check: 0.342 × 0.985 + 0.940 × 0.174 ≈ 0.500, which is 1⁄2.

Concept

The compound-angle formula sin(A + B) = sinA cosB + cosA sinB turns a sum of two products into one sine. The shape to spot: sine times cosine, plus cosine times sine.

With a minus sign the same shape is sin(A − B). The cosine formulas pair like with like: cos(A + B) = cosA cosB − sinA sinB.

Neither sin 20° nor sin 10° is a standard value. That is the signal to combine the angles instead of evaluating each term.

Key facts

sin(A + B) = sinA cosB + cosA sinB.
sin(A − B) = sinA cosB − cosA sinB.
cos(A + B) = cosA cosB − sinA sinB.
sin 30° = 1⁄2, sin 45° = 1⁄√2, sin 60° = √3⁄2.

Study next

tan(A + B) = (tanA + tanB)⁄(1 − tanA tanB)Reading cos 50° cos 10° − sin 50° sin 10° as cos 60°sin 2A = 2 sinA cosA as the case A = B

Common traps

Evaluating sin 20° and sin 10° separately instead of spotting the sin(A + B) pattern
Mixing up the pairings: sinA cosB + cosA sinB is a sine, while cosA cosB − sinA sinB is a cosine

18 Sep 2025, 12:30, Quant Q.14 asks for sin(A + B) from sinA = 3⁄5 and cosB = 12⁄13: (3⁄5)(12⁄13) + (4⁄5)(5⁄13) = 56⁄65, the keyed value.

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 98 SSC CGL questions on it, every solved shift.