SSC CGL 2024 Tier-I · 19 September 2024, Shift 1 · Quantitative Aptitude · Question 4 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 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.

If sinA + cosA = √3, then find the value of tanA + cotA + 2sinAcosA.

(a)2
(b)3
(c)6
(d)1

Answer

Why

Correct — B. Square the given sum first — it hands you sinA cosA in one step.

(sinA + cosA)² = 3
sin²A + cos²A + 2 sinA cosA = 3
1 + 2 sinA cosA = 3 → sinA cosA = 1

tanA + cotA = (sin²A + cos²A) ⁄ (sinA cosA) = 1 ⁄ 1 = 1

Asked value = (tanA + cotA) + 2 sinA cosA
= 1 + 2 = 3 → option (b)

Why the others are wrong

(a)
2 — 2 is the value of 2 sinA cosA alone. Stopping there answers only the tail of the expression and drops the tanA + cotA that stands in front of it.
(c)
6 — 6 is twice the keyed value and no step of the identity doubles anything. The coefficient 2 appears once, inside 2 sinA cosA, and it has already been used.
(d)
1 — 1 is tanA + cotA on its own. It is the harder half of the working, abandoned one term early.

Concept

The engine here is a single identity: tanA + cotA = 1 ⁄ (sinA cosA), because sinA ⁄ cosA + cosA ⁄ sinA collects over the common denominator to (sin²A + cos²A) ⁄ (sinA cosA).

So the whole expression depends on one number, the product sinA cosA, and squaring a sum of sine and cosine is the standard way to expose that product.

Learn the pair together: squaring gives 1 + 2 sinA cosA, and dividing gives 1 ⁄ (sinA cosA). Between them they answer most 'find the value of' items of this shape.

Be honest about the data: sinA + cosA can never exceed √2, so no real angle satisfies sinA + cosA = √3. The item is a formal identity exercise, and the algebra SSC intends still lands cleanly on 3.

Key facts

(sinA + cosA)² = 1 + 2 sinA cosA, since sin²A + cos²A = 1.
tanA + cotA equals 1 ⁄ (sinA cosA) for every angle where both are defined.
The maximum value of sinA + cosA is √2, reached at A = 45°.

Study next

Deriving sinA − cosA from sinA + cosA by squaring and using sin²A + cos²A = 1Expressions built on the product sinA cosA, such as sin⁴A + cos⁴AThe companion identity sec²A − tan²A = 1 in value-finding questions

Common traps

Answering with 2 sinA cosA and forgetting the tanA + cotA term.
Writing tanA + cotA as sinA cosA instead of its reciprocal.
Trying to find the angle A first, which wastes time and cannot succeed here.

SSC gives one combination of sine and cosine and asks for a second that looks unrelated, so the work is to reduce both to sinA cosA.

The reciprocal trick returns at Quant Q.8 in this shift, there with sin x and cosec x.

Related PYQs

No directly related past PYQ was found.