JEE Main 2026 Apr 5 Shift 1, Mathematics Q12: Trigonometric Functions

JEE Main2026Apr 5, Shift 1Mathematics

The sum of all the integral values of $p$ such that the equation $3 sin^{2} x + 12 cos x - 3 = p$ , $x \in R$ , has at least one solution, is :

Solution

$P = 12 cos x - 3 cos^{2} x$

$P = - 3 (cos^{2} x - 4 cos x)$

$P = - 3 ((cos x - 2)^{2} - 4)$

put $\cos x=-1 \Rightarrow P=-15$

put $\cos x=1 \Rightarrow P=9$

$- 15 \leq P \leq 9$

Sum of all integers $= - (10 + 11 + \dots + 15)$ $= - 75$

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.