SSC CGL 2024 Tier-I · 11 September 2024, Shift 1 · Quantitative Aptitude · Question 15 of 95

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

In a ΔABC right-angled at C, if tan A = √3, then the value of sinA cosB cot(A + B) is:

(a)1
(b)2
(c)0
(d)

Answer

Why

Correct — C. The right angle settles it before any values are substituted.

The three angles sum to 180° and C = 90°, so A + B = 90°
cot(A + B) = cot 90° = cos 90° ⁄ sin 90° = 0 ⁄ 1 = 0

The product carries that zero: sin A × cos B × 0 = 0 → option (c)

The given tan A = √3 only fixes A = 60° and B = 30°, giving sin A cos B = (√3⁄2)(√3⁄2) = 3⁄4. And 3⁄4 × 0 is still 0.

Why the others are wrong

(a)
1 — cot 90° is 0, not 1. A student who mis-remembers it as 1 still lands on sin 60° cos 30° = 3⁄4, which is not on the list — a signal that the third factor was mishandled.
(b)
2 — sin A and cos B are each at most 1, so their product cannot reach 2 even before the third factor is applied.
(d)
Option (d) is the image √3 — the value tan A is given as, copied back out. It is the input to the question, not the value of the product.

Concept

Two facts meet here and only one of them decides the answer.

In a triangle right-angled at C, the acute angles are complementary: A + B = 90°. So any function of A + B is a function of 90°, and cot 90° = 0.

A product with a zero factor is zero whatever the other factors are, which makes tan A = √3 decoration. Looking for the collapsing factor first saves the whole computation.

The stem is printed as an image on the response sheet and reads: 'In a △ABC right-angled at C, if tan A = √3, then the value of sinA cosB cot(A + B) is:'.

Option (d) is also an image, showing √3; options (a), (b) and (c) are the plain numbers 1, 2 and 0.

Key facts

In a right triangle the two acute angles are complementary, so A + B = 90°.
cot 90° = cos 90° ⁄ sin 90° = 0.
tan A = √3 gives A = 60° for an acute angle, so B = 30°.
Any product containing a zero factor is zero, whatever the other factors evaluate to.

Study next

Complementary-angle identities such as sin(90° − θ) = cos θStandard values of tan, cot, sec and cosec at 0°, 30°, 45°, 60° and 90°Right-triangle trigonometry when one acute angle is given as a ratio

Common traps

Working out sin 60° cos 30° = 3⁄4 and stopping before the third factor.
Calling cot 90° undefined, when it is tan 90° that has no value.
Assuming the right angle sits at A because the question opens with tan A.

Look for the factor that collapses before starting any algebra.

Complementary angles do the same work at 26 Sep 2024, 09:00, Quant Q.10: sin(48° + k) = cos 13° forces 48° + k = 77°, so k = 29.

At 25 Sep 2024, 12:30, Quant Q.5 the whole of tan 72° − tan 27° − tan 72° tan 27° collapses to 1 through the tan(A − B) identity, without a single value being substituted.

Related PYQs

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