Option (b) prints **sec 55°**. No secant is created anywhere: the co-function step turns cot 35° into tan 55° and the two tangents then cancel outright.

Option (c) prints **0**. A quotient is zero only when its numerator is, and tan 55° is roughly **1.43**.

Option (d) prints **cos 35°**. Complementary work does swap sine with cosine, but this expression is a tangent over a cotangent, and it cancels to a pure number.

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SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 5 of 99

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.

Find the value of .

Answer

Why

Correct — A. The two angles add to 90°, which is the signal to use a co-function identity.

Rule: cot θ = tan(90° − θ)
cot 35° = tan(90° − 35°) = tan 55°

tan 55° ⁄ cot 35° = tan 55° ⁄ tan 55°
= 1 → option (a), which prints the numeral 1.

Why the others are wrong

(b)
Option (b) prints sec 55°. No secant is created anywhere: the co-function step turns cot 35° into tan 55° and the two tangents then cancel outright.
(c)
Option (c) prints 0. A quotient is zero only when its numerator is, and tan 55° is roughly 1.43.
(d)
Option (d) prints cos 35°. Complementary work does swap sine with cosine, but this expression is a tangent over a cotangent, and it cancels to a pure number.

Concept

Complementary angles sum to 90°, and each ratio turns into its co-ratio across that gap:

sin θ = cos(90° − θ), tan θ = cot(90° − θ), sec θ = cosec(90° − θ)

So the moment 55° and 35° appear in one expression, check whether the pair is meant to collapse. Here it collapses completely: numerator and denominator are the same number written two ways, so the quotient is 1 whatever tan 55° happens to equal.

The four choices are printed as pictures rather than text. Option (a) is the numeral 1, option (b) is sec 55°, option (c) is 0 and option (d) is cos 35°.

Key facts

cot θ = tan(90° − θ), so cot 35° and tan 55° are the same number.
55° + 35° = 90°, the flag that a complementary-angle identity is intended.
The complementary pairs are sine with cosine, tangent with cotangent, and secant with cosecant.

Study next

Converting ratios of angles above 45° into ratios below 45° with the 90° − θ ruleAllied angles past the complement: 90° + θ and 180° − θ, and the sign each carriestan θ × cot θ = 1, a different pairing from tan θ = cot(90° − θ)

Common traps

Reaching for a decimal value of tan 55° instead of noticing that 55 and 35 are complements
Confusing cot 35° = tan 55° with cot 35° = 1⁄tan 35°, which is true but cancels nothing here

This one is printed as a bare 'Find the value of', with the expression and all four options pushed into images.

The same co-function cancellation is set as a subtraction at 11 Sep 2024, 09:00, Quant Q.5 — sec 35° ⁄ cosec 55° − cos 25° ⁄ sin 65°, two complementary pairs — and as a product at 11 Sep 2024, 12:30, Quant Q.12, which is cosec 56° cos 34° − cos 59° cosec 31°.

It is asked openly at 11 Sep 2024, 16:00, Quant Q.7 — express sin 74° + tan 74° in ratios of angles between 0° and 45° — and it drives the allied-angle expression at 17 Sep 2024, 12:30, Quant Q.17, built from cos(90 − θ) and sin(90 + θ).

Related PYQs

No directly related past PYQ was found.