SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 18 of 100

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.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

If sin A = 3⁄5 and A lies in the 2nd quadrant, what is the value of tan A?

(a)−3⁄4
(b)−2⁄5
(c)2⁄5
(d)7⁄5

Answer

Why

Correct — A. Get the size of cos A from the identity, then its sign from the quadrant.

cos²A = 1 − sin²A = 1 − 9⁄25 = 16⁄25
cos A = ±4⁄5, and cos is negative in the 2nd quadrant, so cos A = −4⁄5

tan A = sin A ÷ cos A = (3⁄5) ÷ (−4⁄5)
= −3⁄4 → option (a)

Why the others are wrong

(b)
−2⁄5 — −2⁄5 has the right sign but an impossible size. It would need cos A = sin A ÷ tan A = (3⁄5) ÷ (−2⁄5) = −3⁄2, and no cosine lies outside −1 to 1.
(c)
2⁄5 — A positive tangent cannot occur in the 2nd quadrant: sin is positive there and cos negative, so their ratio is negative. 2⁄5 would also need cos A = 3⁄2.
(d)
7⁄5 — 7⁄5 is sin A − cos A = 3⁄5 + 4⁄5, a difference, not the ratio sin A ÷ cos A. It is also positive, and tan is negative in the 2nd quadrant.

Concept

The identity sin²A + cos²A = 1 gives the size of cos A but never its sign. Here the numbers are the 3-4-5 triangle, so the size is 4⁄5.

The sign comes from the quadrant. By the ASTC rule, all ratios are positive in the 1st quadrant, only sin and cosec in the 2nd, tan and cot in the 3rd, cos and sec in the 4th.

Options (a) and (b) are both negative. The sign rule removes (c) and (d); the 3-4-5 triangle decides between the two that are left.

Key facts

In the 2nd quadrant (90° < A < 180°) sin and cosec are positive, and cos, sec, tan and cot are negative.
sin²A + cos²A = 1 for every angle A.
tan A = sin A ÷ cos A.
With sin A = 3⁄5 in the 2nd quadrant, cos A = −4⁄5 and tan A = −3⁄4.

Study next

Signs of the six ratios in each quadrant (ASTC)Pythagorean triplets in trigonometry: 3-4-5, 5-12-13, 8-15-17Finding sec A or cot A from one ratio and its quadrant

Common traps

Reading cos A = +4⁄5 straight off the 3-4-5 triangle, which gives tan A = +3⁄4 with the wrong sign.
Remembering that sin is positive in the 2nd quadrant but forgetting that tan, being sin ÷ cos, is negative there.

The same data, sin A = 3⁄5 in the second quadrant, is asked 17 Sep 2025, 16:00, Quant Q.14 for (sin A + cos A)² = (3⁄5 − 4⁄5)² = 1⁄25.

22 Sep 2025, 09:00, Quant Q.17 gives sin A = 5⁄13 in the 2nd quadrant and asks sin A × sec A, which is tan A = −5⁄12.

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.