SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 19 of 99

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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If sin A = 0.6 and cos A = 0.8, what is tan A?

(a)0.56
(b)0.75
(c)0.45
(d)0.52

Answer

Why

Correct — B.
Definition: tan A = sin A ⁄ cos A
Substitute: = 0.6 ⁄ 0.8
Clear the decimals: = 6⁄8 = 3⁄4

Check: tan A × cos A = 0.75 × 0.8 = 0.6 = sin A
Convert: 3⁄4 = 0.75 → option (b)

Why the others are wrong

(a)
0.56 — 0.56 is smaller than 0.6, but dividing 0.6 by 0.8, a number below 1, must give more than 0.6. Check: 0.56 × 0.8 = 0.448, not 0.6.
(c)
0.45 — 0.45 is below 0.6, so it cannot be 0.6 divided by 0.8. Check: 0.45 × 0.8 = 0.36, not 0.6.
(d)
0.52 — 0.52 is also below 0.6, so it cannot be 0.6 ⁄ 0.8. Check: 0.52 × 0.8 = 0.416, not 0.6.

Concept

tan A = sin A ⁄ cos A is a definition, so when both sin A and cos A are given, tan A is one division away.

The pair 0.6 and 0.8 is the 3-4-5 right triangle in decimals: opposite 3, adjacent 4, hypotenuse 5 gives sin A = 3⁄5, cos A = 4⁄5 and tan A = 3⁄4. Spotting the triple turns the decimals into fractions you already know.

The two values are consistent: 0.6² + 0.8² = 0.36 + 0.64 = 1, so they can be the sine and cosine of the same angle.

Key facts

tan A = sin A ⁄ cos A and cot A = cos A ⁄ sin A
sin A = 3⁄5 and cos A = 4⁄5 give tan A = 3⁄4
Dividing by a number between 0 and 1 makes the result larger, so 0.6 ⁄ 0.8 must exceed 0.6

Study next

The 5-12-13 and 8-15-17 triples as sine and cosine pairsFinding cos A when only sin A is given: cos A = √(1 − sin²A) for acute ADouble-angle values from a 3-4-5 angle: sin 2A = 2 sin A cos A

Common traps

Inverting the ratio: 0.8 ⁄ 0.6 ≈ 1.33 is cot A, not tan A.
Multiplying sin A by cos A (0.48) instead of dividing.

The same 0.6 and 0.8 pair is set at 20 Sep 2025, 09:00, Quant Q.24, where sin x = 0.6 leads to sin 2x + cos 2x. The tan = sin ⁄ cos step in algebraic form is at 26 Sep 2025, 12:30, Quant Q.19 (sin A = 2x⁄(1+x²), find tan A).

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 131 SSC CGL questions on it, every solved shift.