SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 20 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 sin x = cos(2x − 10°), find the value of x.

(a)25.52°
(b)33.33°
(c)40°
(d)50°

Answer

Why

Correct — B. If sin P = cos Q with both angles acute, then P + Q = 90°.

Set up: x + (2x − 10°) = 90°
Collect: 3x − 10° = 90°
Add 10°: 3x = 100°
Divide by 3: x = 100⁄3 ≈ 33.33° → option (b)

Check: 2x − 10° = 56.67°, and 33.33° + 56.67° = 90°.

Why the others are wrong

(a)
25.52° — 25.52° gives 2x − 10° = 41.04°, and 25.52° + 41.04° = 66.56°. The two angles are not complementary, so sin x ≠ cos(2x − 10°).
(c)
40° — 40° gives 2x − 10° = 70°, and 40° + 70° = 110°, not 90°. Numerically, sin 40° ≈ 0.643 while cos 70° ≈ 0.342.
(d)
50° — 50° makes 2x − 10° = 90°, so the right side is cos 90° = 0, while sin 50° ≈ 0.766.

Concept

The co-function identity is sin θ = cos(90° − θ). So when sin P = cos Q with P and Q acute, Q = 90° − P, that is P + Q = 90°.

Once both angles are written in terms of x, the trigonometry is gone and a linear equation is left.

The stem does not say the angles are acute. That is the standard reading, and among the four options 33.33° is the value that satisfies the equation. The key is 100⁄3 rounded to two decimals.

Key facts

sin θ = cos(90° − θ) and cos θ = sin(90° − θ).
If sin P = cos Q with P and Q acute, then P + Q = 90°.
tan P = cot Q and sec P = cosec Q also give P + Q = 90° for acute angles.
100⁄3 = 33.33 to two decimal places.

Study next

tan A = cot B and sec A = cosec B, which also give A + B = 90°Complementary-angle simplification such as sin 25° ÷ cos 65°Standard values of sin, cos and tan at 30°, 45° and 60°

Common traps

Setting x = 2x − 10° as if sin and cos were the same function, which gives x = 10°.
Writing the sum as 180° instead of 90°, which gives 3x = 190° and x = 63.33°.

24 Sep 2025, 16:00, Quant Q.22 uses the same set-up with 3x: sin(x) = cos(3x − 30°) gives 4x − 30° = 90°, so x = 30°.

24 Sep 2024, 09:00, Quant Q.22 asks sin 3A = cos(A − 26°) with 3A acute: 4A − 26° = 90°, so A = 29°.

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.