SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 12 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.

Evaluate the value of (cosec56° cos34° − cos59° cosec31°).

Answer

Why

Correct — B. Both angle pairs are complementary, so each product collapses to 1.

34° + 56° = 90°, so cos34° = sin56°
cosec56° × cos34° = sin56° ⁄ sin56° = 1

31° + 59° = 90°, so cos59° = sin31°
cos59° × cosec31° = sin31° ⁄ sin31° = 1

1 − 1 = 0, which is what option (b) shows.

Why the others are wrong

(a)
Option (a) shows 2, the value of the two products added. The bracket subtracts the second from the first, and 1 − 1 is 0.
(c)
Option (c) shows 1, the value of either product taken alone. Both products equal 1, so simplifying one and stopping leaves the subtraction undone.
(d)
Option (d) shows −1, which would need the second product to be 2 while the first is 1. Both are exactly 1, because both angle pairs sum to 90°.

Concept

Ratios of complementary angles convert into each other: sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, cosec(90° − θ) = sec θ.

The exam use is narrower than that list looks. When the two angles inside a product add to 90°, rewrite one of them so both terms carry the same ratio of the same angle, and the product cancels to 1.

Here 56° + 34° = 90° and 59° + 31° = 90°, so no angle value is ever needed.

The four options are printed as images. Reading (a) to (d) they are 2, 0, 1 and −1, so the card names each option by what its picture shows.

Key facts

cos(90° − θ) = sin θ, and cosec θ = 1 ⁄ sin θ.
56° + 34° = 90°, so cosec56° × cos34° = 1.
59° + 31° = 90°, so cos59° × cosec31° = 1.

Study next

Complementary-angle identities for tan, cot, sec and cosecSimplifying sec and cosec products inside a single bracketStandard angle values at 0°, 30°, 45°, 60° and 90°

Common traps

Adding the two products instead of subtracting them.
Converting only one of the two angles and leaving a mismatched ratio.
Hunting for standard-angle values when 56° and 31° are not standard angles.

SSC builds these from angle pairs that sum to 90° and disguises them with non-standard angles such as 56° and 34°. The first move on any such bracket is to add the angles.

Related PYQs

No directly related past PYQ was found.