JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q12

← JEE Main 2026 · 8 Apr · Shift 2

MathematicsSingle correct+4 / -1Question 12 of 75

Let $\alpha=3\sin^{-1}\left(\dfrac6{11}\right)$ and $\beta=3\cos^{-1}\left(\dfrac49\right)$ , where inverse trigonometric functions take only the principal values.

Given below are two statements :

Statement I : $\cos(\alpha+\beta)>0$ .

Statement II : $\cos(\alpha)<0$ .

In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Answer and worked solution

Official answer: A

Angles.

$\sin^{-1}\tfrac6{11}\approx33.1^\circ$ , so $\alpha\approx99.2^\circ$ and $\cos\alpha<0$ : II is true.
$\cos^{-1}\tfrac49\approx63.6^\circ$ , so $\beta\approx190.8^\circ$ .

Sum. $\alpha+\beta\approx290^\circ$ , in the fourth quadrant, so $\cos(\alpha+\beta)>0$ : I is true.

(A)

Topics:Inverse trigonometric functions

← Previous question Next question →

JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 12