Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Trigonometric Equations

NDA 2024 · Mathematics · Trigonometric Equations

What is the number of solutions of the equation 2 x · 3 x=1 for 0 <...

What is the number of solutions of the equation cot⁡2x⋅cot⁡3x=1\cot 2 x \cdot \cot 3 x=1 for 0<x<π?0 < x < \pi ?

Options

  1. AOnly one
  2. BOnly two
  3. COnly five
  4. DMore than five

Correct answer

C. Only five

Step-by-step solution

We have given, cot⁡2x⋅cot⁡3x=1\cot 2 x \cdot \cot 3 x=1 (given) ⇒cos⁡2x⋅cot⁡3x−sin⁡2x⋅sin⁡3x=0⇒cos⁡(2x+3x)=cos⁡5x=0\begin{aligned} & \Rightarrow \cos 2 x \cdot \cot 3 x-\sin 2 x \cdot \sin 3 x=0 \\ & \Rightarrow \cos (2 x+3 x)=\cos 5 x=0 \end{aligned} Hence 5x=π2,3π2,5π2,7π2,9π2,…5 x=\frac{\pi}{2}, \frac{3 \pi}{2}, \frac{5 \pi}{2}, \frac{7 \pi}{2}, \frac{9 \pi}{2}, \ldots But 0<x<π⇒x=π10,3π10,5π10,7π10,9π100 < x < \pi\Rightarrow \mathrm{x}=\frac{\pi}{10}, \frac{3 \pi}{10}, \frac{5 \pi}{10}, \frac{7 \pi}{10}, \frac{9 \pi}{10} Thus only five values of xx are possible.
Practice Trigonometric Equations on Quantrex Academy →

More from Trigonometric Equations

What is the smallest positive x satisfying _ x x+ _ x x=2 ? NDA 2026If 0 ≤ x ≤ (π)/(2) , then what is the number of values of x satisfying the equation x + x… NDA 2025For the following two (02) items: Let (2x + 3y) = (1)/(2) and (3x + 2y) = 3 2 , where -π… NDA 2025For the following two (02) items: Let (2x + 3y) = (1)/(2) and (3x + 2y) = 3 2 , where -π… NDA 2025What is the general solution of ^ 100 x- ^ 100 x=1 ? where n is an integer. NDA 2024If (π θ)= (π θ), 0 θ (π)/(2) ; then what is the value of 8 ^2(θ+(π)/(4)) NDA 2023If 1+2( x+ x)( x- x)=0 where 0 < x < 360^ ^ ∘ , then how many values does x take? NDA 2022Let 4 ^2 x=3 , where 0 ≤ x ≤ π . What is 3 x equal to? NDA 2021The value of x , satisfying the equation _ x x=1 , where 0 < x < (π)/(2) , is NDA 2021A is an angle in the fourth quadrant. If satisfies the trigonometric equation 3(3- ^2 A… NDA 2018What is/are the solutions of the trigonometric equation cosec x+ x= 3 , where 0 < x < 2 π… NDA 2018Consider the equation: k x+ 2 x=2 k-7 If the equation possesses solution, then what is… NDA 2016Consider the equation: k x+ 2 x=2 k-7 If the equation possesses solution, then what is… NDA 2016Which one of the following is one of the solutions of the equation 2 θ · θ=1 ? NDA 2014The complete solution of 3 ^2 x=1 is given by: NDA 2014 Full Trigonometric Equations list Trigonometric Equations JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs