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JEE Main 202126 FebruaryMorning Shift

Exam: JEE Main
Year: 2021
Date: 26 February
Shift: Morning Shift
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Main 2021 · 26 February · Morning Shift · Mathematics · Trigonometric Ratios & Identities

The number of integral values of k for which the equation 3 x + 4 x...

The number of integral values of

k

for which the equation

3\sin x + 4\cos x = k + 1

has a solution,

k \in R

is _______.

Correct answer

0

Step-by-step solution

3\sin x + 4\cos x = k + 1

$⇒ k + 1 \in \left[- \sqrt{{3}^{2} + {4}^{2}}, \sqrt{{3}^{2} + {4}^{2}}\right]$

$⇒ k + 1 \in \left[- 5, 5\right]$

$⇒ k \in \left[- 6, 4\right]$

No. of integral values of $k = 11$

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