SSC CGL 2024 Tier-I · 11 September 2024, Shift 3 · Quantitative Aptitude · Question 7 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.

Express sin 74° + tan 74° in terms of trigonometric ratios of angles between 0° and 45°.

Answer

Why

Correct — C. The four options are images; option (c) reads cos 16° + cot 16°.

Write 74° as a complement: 74° = 90° − 16°.

sin(90° − θ) = cos θ, so sin 74° = cos 16°
tan(90° − θ) = cot θ, so tan 74° = cot 16°

sin 74° + tan 74° = cos 16° + cot 16° → option (c), and 16° lies in the required 0°–45° range.

Why the others are wrong

(a)
Option (a) reads cosec 16° + sec 16°. That is the rewriting of sec 74° + cosec 74°, because sec(90° − θ) = cosec θ. The stem starts from sin and tan.
(b)
Option (b) reads cosec 16° + cot 16°. The cot half is right; the first term is not, since cosec 16° equals sec 74°, whereas sin 74° equals cos 16°.
(d)
Option (d) reads sec 16° + cot 16°. sec 16° is cosec 74°, the reciprocal of sin 74° rather than sin 74° itself, so the first term is inverted.

Concept

Complementary angles pair the six ratios into three couples: sin with cos, tan with cot, sec with cosec. For any θ, sin(90° − θ) = cos θ, tan(90° − θ) = cot θ and sec(90° − θ) = cosec θ.

That is what lets any angle between 45° and 90° be rewritten below 45°. Since 74° = 90° − 16°, every ratio of 74° has a twin at 16°.

The reciprocal pairs are a different relationship and are easy to confuse with these. sin and cosec are reciprocals; sin and cos are complements.

A numerical check settles it in seconds: sin 74° ≈ 0.961 and tan 74° ≈ 3.487, summing to about 4.449, while cos 16° ≈ 0.961 and cot 16° ≈ 3.487.

Key facts

sin(90° − θ) = cos θ and cos(90° − θ) = sin θ.
tan(90° − θ) = cot θ and cot(90° − θ) = tan θ.
sec(90° − θ) = cosec θ and cosec(90° − θ) = sec θ.
74° = 90° − 16°, so sin 74° = cos 16° and tan 74° = cot 16°.

Study next

Complementary-angle identities for all six trigonometric ratiosTelling complements apart from reciprocalsCompound-angle results where two given angles differ by 45°

Common traps

Confusing the complement with the reciprocal and turning sin 74° into cosec 16°.
Subtracting from 180° instead of 90°, which changes the sign rather than the ratio.
Converting sin correctly and then leaving tan 74° untouched.

The same identity appears as an equation to solve at 26 Sep 2024, 09:00, Quant Q.10 — sin(48° + k) = cos 13°, find k — where you set (48 + k) + 13 = 90.

25 Sep 2024, 12:30, Quant Q.5 pushes into compound angles with tan 72° − tan 27° − tan 72° tan 27°, where the work is done by 72° − 27° = 45°.

Related PYQs

No directly related past PYQ was found.