Option (a) shows **√3⁄2**, which is cos 30°. That is the value of a single cosine, and 30° plays no part in this expression.

Option (b) shows **2**, which would need both squares to equal 1, i.e. both angles to be 0°. In fact cos²29° ≈ 0.765 and cos²61° ≈ 0.235.

Option (c) shows **0**, which would need both cosines to vanish — that happens only at 90°. Each squared term here is positive.

Join @UPSCneil — Free Guidance

SSC CGL 2024 Tier-I · 9 September 2024, Shift 1 · Quantitative Aptitude · Question 2 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.

The value of is:

Answer

Why

Correct — D. The stem image reads cos²29° + cos²61°, and the two angles add to 90°.

61° = 90° − 29°, so cos 61° = cos(90° − 29°) = sin 29°.

Substitute:
cos²29° + cos²61° = cos²29° + sin²29°

Apply sin²θ + cos²θ = 1:
= 1 → option (d), the picture showing the numeral 1.

Why the others are wrong

(a)
Option (a) shows √3⁄2, which is cos 30°. That is the value of a single cosine, and 30° plays no part in this expression.
(b)
Option (b) shows 2, which would need both squares to equal 1, i.e. both angles to be 0°. In fact cos²29° ≈ 0.765 and cos²61° ≈ 0.235.
(c)
Option (c) shows 0, which would need both cosines to vanish — that happens only at 90°. Each squared term here is positive.

Concept

Two angles that sum to 90° are complementary, and the identity that follows is cos(90° − θ) = sin θ.

Spot the pair — 29 + 61 = 90 — and a two-term expression collapses onto sin²θ + cos²θ = 1 with no numerical work at all.

The same conversion settles sin²18° + sin²72° = 1 and tan 35° × tan 55° = 1: in each case the second angle is the complement of the first.

The expression and all four options arrive as images in the response sheet, so the printed stem reads only 'The value of is:'. The options are, in order, √3⁄2, 2, 0 and 1.

Key facts

cos(90° − θ) = sin θ, so cos 61° = sin 29°.
sin²θ + cos²θ = 1 holds for every angle θ.
cos²29° + cos²61° = 1 exactly, because 29° + 61° = 90°.

Study next

Complementary-angle conversions for tan and cot, where tan(90° − θ) = cot θExpressions of the form sin²A + sin²B in which A + B = 90°Standard values of sin, cos and tan at 0°, 30°, 45°, 60° and 90°

Common traps

Reaching for decimal values of cos 29° and cos 61° instead of noticing that they add to 90°
Misreading the option pictures, since (c) is a 0 and (d) is a 1 in images of the same size

The angles are chosen so the arithmetic disappears and the whole item is one identity. Read the option images before choosing here — 0 and 1 sit next to each other.

Related PYQs

No directly related past PYQ was found.