SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 22 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 13 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.

If sinA + cosA = 5⁄4, find sin2A.

(a)1⁄4
(b)5⁄18
(c)7⁄8
(d)9⁄16

Answer

Why

Correct — D.
Square both sides: (sinA + cosA)² = (5⁄4)² = 25⁄16
Expand: sin²A + cos²A + 2 sinA cosA = 25⁄16
Use sin²A + cos²A = 1: 1 + 2 sinA cosA = 25⁄16

Subtract 1: 2 sinA cosA = 25⁄16 − 16⁄16 = 9⁄16
Since sin2A = 2 sinA cosA, sin2A = 9⁄16 → option (d)

Why the others are wrong

(a)
1⁄4 — 1⁄4 is 5⁄4 − 1, found by subtracting 1 without squaring first. The identity needs (5⁄4)² = 25⁄16, and 25⁄16 − 1 = 9⁄16.
(b)
5⁄18 — 5⁄18 would need (sinA + cosA)² = 1 + 5⁄18 = 23⁄18, but (5⁄4)² is 25⁄16, so 5⁄18 is not 2 sinA cosA.
(c)
7⁄8 — 7⁄8 would need (sinA + cosA)² = 1 + 7⁄8 = 15⁄8, but (5⁄4)² is 25⁄16, so 7⁄8 is not 2 sinA cosA.

Concept

When a question hands you sinA + cosA, square it. The square always splits the same way: sin²A + cos²A, which is 1, plus 2 sinA cosA.

So (sinA + cosA)² = 1 + 2 sinA cosA, and 2 sinA cosA is exactly sin2A. One squaring turns the given sum into the double angle without ever finding A.

The given value is possible: sinA + cosA can be at most √2 ≈ 1.414, and 5⁄4 = 1.25 is below that. The same squaring also gives (sinA − cosA)² = 1 − 9⁄16 = 7⁄16.

Key facts

sin²A + cos²A = 1 for every angle A.
sin2A = 2 sinA cosA.
(sinA + cosA)² = 1 + sin2A and (sinA − cosA)² = 1 − sin2A.
sinA + cosA never exceeds √2.

Study next

Finding sin⁴A + cos⁴A from sinA + cosA, using sin⁴A + cos⁴A = 1 − 2 sin²A cos²ADouble-angle forms of cos2A: cos²A − sin²A = 1 − 2 sin²A = 2 cos²A − 1Rewriting tanA + cotA as 1 ⁄ (sinA cosA)

Common traps

Subtracting 1 from 5⁄4 before squaring, which gives 1⁄4 instead of 9⁄16
Stopping at sinA cosA = 9⁄32 when the question asks for sin2A, which is twice that

19 Sep 2025, 09:00, Quant Q.14 runs the same identity backwards: tanA + cotA = 2 gives sinA cosA = 1⁄2, so (sinA + cosA)² = 2 and sinA + cosA = √2. 21 Sep 2025, 09:00, Quant Q.18 squares sin A + cos A = 1 to find sin⁴A + cos⁴A, keyed 1.

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 131 SSC CGL questions on it, every solved shift.