SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 20 of 95

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.

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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 tan A = cot(2A − 30°), then what is the value of A?

(a)30°
(b)25°
(c)18°
(d)40°

Answer

Why

Correct — D.
Rule: tan A = cot(90° − A), so tan A = cot B with both angles acute means A + B = 90°.

Set the angles complementary: A + (2A − 30°) = 90°
Combine: 3A − 30° = 90°
Add 30°: 3A = 120°
Divide by 3: A = 40° → option (d)

Check: 2 × 40° − 30° = 50°, and 40° + 50° = 90°.

Why the others are wrong

(a)
30° — 30° solves A = 2A − 30°, which treats tan and cot as the same ratio. Then both angles are 30°, and tan 30° = 1⁄√3 while cot 30° = √3.
(b)
25° — With A = 25°, 2A − 30° = 20°. The two angles add to 45°, not 90°, so tan 25° ≠ cot 20°.
(c)
18° — With A = 18°, 2A − 30° = 6°. The two angles add to only 24°, so tan 18° is nowhere near cot 6°.

Concept

Co-function identities pair each ratio with its partner at the complementary angle: sin θ = cos(90° − θ), tan θ = cot(90° − θ), sec θ = cosec(90° − θ).

So when tan of one acute angle equals cot of another, the two angles must add to 90°. That turns a trigonometric equation into a linear one in A.

Strictly, tan A = cot B holds whenever A + B = 90° + k × 180°. The stem does not say the angles are acute, but all four options are acute and A = 40° keeps both angles acute (40° and 50°).

Key facts

tan θ = cot(90° − θ) and sin θ = cos(90° − θ).
If tan A = cot B with A and B acute, then A + B = 90°.
Here A = 40° and 2A − 30° = 50°, a complementary pair.

Study next

sin A = cos B for acute angles, which also gives A + B = 90°sec A = cosec B and the same complementary ruleProducts such as tan 1° × tan 2° × … × tan 89° = 1, built on tan θ × tan(90° − θ) = 1

Common traps

Setting A = 2A − 30°, as if tan and cot were the same ratio, which gives 30°.
Adding the angles to 180° instead of 90°: 3A − 30° = 180° gives A = 70°.

The stem ties tan A to cot of an expression in A and asks for A. The same complementary-angle step settles 24 Sep 2024, 09:00, Quant Q.22, where sin 3A = cos(A − 26°) gives 4A − 26° = 90° and 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.