If A + B + C = π (A, B, C > 0) and the angle C is obtuse, then which of the following is/are correct? I. sin A ⋅ sin B 1 Select the answer using the code given below:

CDS 2026 PYQ with Answer — If A + B + C = π (A, B, C > 0) and the angle C is obtuse, then which…

2026 · Q48

If A + B + C = π (A, B, C > 0) and the angle C is obtuse, then which of the following is/are correct? I. sin A ⋅ sin B < 1 II. tan A ⋅ tan B > 1 Select the answer using the code given below:

Elementary MathematicsTrigonometry

AI only
BII only
CBoth I and II
DNeither I nor II

Explanation

Since C is obtuse, A + B < 90° with A, B > 0. Statement I: sin A and sin B are each in (0, 1), so their product is below 1 — correct. Statement II: tan(A + B) = (tan A + tan B)/(1 − tan Atan B) > 0 with positive numerator forces 1 − tan Atan B > 0, i.e. tan Atan B < 1 — so statement II is false. Hence I only, option A.