SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 13 of 100

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 6 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.

(3 sin 58°) ⁄ (5 cos 32°) + (2 cos 62°) ⁄ (5 sin 28°) is equal to:

(a)2
(b)0
(c)1
(d)3

Answer

Why

Correct — C. The question is an image: it asks for the value of (3 sin 58°)/(5 cos 32°) + (2 cos 62°)/(5 sin 28°).

Use the complementary rule sin θ = cos (90° − θ).

58 + 32 = 90, so sin 58° = cos 32° and the first fraction is 3/5.
62 + 28 = 90, so cos 62° = sin 28° and the second fraction is 2/5.

3/5 + 2/5 = 1 → option (c)

Why the others are wrong

(a)
2 — 2 comes from cancelling each fraction all the way to 1 and adding. Only the trigonometric ratios cancel — the coefficients 3/5 and 2/5 survive, and they sum to 1.
(b)
0 — 0 would need the two terms to cancel each other, which requires a minus sign between them. The image shows a plus, and both terms are positive.
(d)
3 — 3 is the first term's numerator kept whole. Cancelling sin 58° against cos 32° leaves 3/5, because the 5 in that denominator has nothing to cancel against.

Concept

Complementary-angle identities let you swap a ratio for its co-ratio whenever two angles add to 90°: sin θ = cos (90° − θ), cos θ = sin (90° − θ), tan θ = cot (90° − θ).

Spotting them is just adding the two angles inside a fraction. Here 58 + 32 = 90 and 62 + 28 = 90, so both fractions collapse to their coefficients before any real calculation.

What is left is fraction addition with a common denominator of 5.

None of 58°, 32°, 62° or 28° is a standard angle with a value you could recall. That is the signal: the item is not asking you to evaluate anything, only to notice the pairs.

Key facts

sin θ = cos (90° − θ), which makes sin 58° equal to cos 32°.
cos θ = sin (90° − θ), which makes cos 62° equal to sin 28°.
Each fraction therefore reduces to its coefficient, 3/5 and 2/5, and these add to exactly 1.

Study next

Complementary-angle identities for tan, cot, sec and cosecExpressions mixing sec θ with cosec (90° − θ) in the same fractionStandard-angle values needed when no complementary pair is present

Common traps

Reaching for approximate sine values instead of checking whether the two angles add to 90°
Cancelling the numerical coefficients along with the trigonometric ratios
Treating sin 58°/cos 32° as an unresolvable non-standard ratio when it is simply 1

The whole item reaches the candidate as an image in the response sheet, so read the angle pairs before anything else.

These items reward recognition rather than computation: the moment two angles in a fraction add to 90°, that fraction is finished.

Related PYQs

No directly related past PYQ was found.