Mathematics · Trigonometry Ratios and Identities

JEE Main 2026 — 5 April, Morning Shift — Question 35

The sum of all the integral values of $p$ such that the equation $3 sin² x + 12 cos x - 3 = p, x∈R,$ has at least one solution, is :

Option A:
$-54$
Option B:
$-60$
Option C:
$-75$
Correct
Option D:
$-84$

Answer: C

Step-by-step solution

$P=12 \cos x-3 \cos ^{2} x$ $P=-3\left(\cos ^{2} x-4 \cos x\right)$ $\mathrm{P}=-3\left((\cos \mathrm{x}-2)^{2}-2\right)$ put $\cos \mathrm{x}=-1 \Rightarrow \mathrm{P}=-15$ put $\cos \mathrm{x}=1 \Rightarrow \mathrm{P}=9$ $-15 \leq \mathrm{P} \leq 9$ Sum of all integers $=-(10+11+\ldots+15)=-75$

Answer key and solution verified before publishing.

Practise Trigonometry Ratios and Identities

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 5 April, Morning Shift
Subject: Mathematics
Chapter: Trigonometry Ratios and Identities
Topic: Maximum and Minimum values of Trigonometric Expressions

If pi/4+sum p=1^11 tan ^-1 (frac2^p-11+2^2 p-1 )=alpha , then tan alpha is equal to \ \ \ \ .

Answer: C

Step-by-step solution

Practise Trigonometry Ratios and Identities

More Trigonometry Ratios and Identities questions from this paper