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JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2024 · 9 April · Evening Shift · Mathematics · Inverse Trigonometric Functions

Let the inverse trigonometric functions take principal values. The...

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin⁡−1x+3cos⁡−1x=2π52 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5}, is _______

Correct answer

0

Step-by-step solution

2sin⁡−1x+3cos⁡−1x=2π5⇒π+cos⁡−1x=2π5⇒cos⁡−1x=−3π5\begin{aligned} & 2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5} \\ & \Rightarrow \quad \pi+\cos ^{-1} x=\frac{2 \pi}{5} \\ & \Rightarrow \quad \cos ^{-1} x=\frac{-3 \pi}{5} \end{aligned}
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