0

Guest

Courses New

Find the value of x between 0 and 2 pi satisfying Cos3x + cos2x = sin 3x/2 + sin x/2

Find the value of x between 0 and 2 pi satisfying 
Cos3x + cos2x = sin 3x/2 + sin x/2

Grade:11

3 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
562-825_Capture.PNG
Aarushi Ahlawat
41 Points
5 years ago
First convert both the sides in multiplication form and then take common to get two factors. Now find the solutions for each of the factor over the given domain
.
cos(3x)+cos(2x)=sin\left ( \frac{3x}{2} \right )+sin\left ( \frac{x}{2} \right )
2cos\left ( \frac{3x+2x}{2} \right )cos\left ( \frac{3x-2x}{2} \right )=2sin\left ( \frac{\frac{3x}{2}+\frac{x}{2}}{2} \right )cos\left ( \frac{\frac{3x}{2}-\frac{x}{2}}{2} \right )
 
cos\left ( \frac{5x}{2} \right )cos\left ( \frac{x}{2} \right )=sin\left ( x \right )cos\left ( \frac{x}{2} \right )
cos\left ( \frac{x}{2} \right ) \left ( cos\left ( \frac{5x}{2} \right )- sin\left ( x \right ) \right )=0
cos\left ( \frac{x}{2} \right ) \left ( cos\left ( \frac{5x}{2} \right )- cos\left (\frac{\pi }{2} - x \right ) \right )=0
OR
cos\left ( \frac{x}{2} \right ) \left ( cos\left ( \frac{5x}{2} \right )- cos\left (\frac{3 \pi }{2} + x \right ) \right )=0
Now the solutions:
If
 
cos\left ( \frac{x}{2} \right ) = 0
x=\pi
 
if
cos\left ( \frac{5x}{2} \right )-cos\left ( \frac{\pi}{2}-x \right )=0
x=\frac{\pi}{7}
and if
 
cos\left ( \frac{5x}{2} \right )-cos\left ( \frac{3\pi}{2}+x \right )=0
 
x=\pi
 
Hence possible values of x between 0 and 2pi are   
 
\frac{\pi}{7} ~ and ~ \pi
 
 
 
Aarushi Ahlawat
41 Points
5 years ago
Above mentioned general solution in answer 1 are not correct for all values of n and for + and -.
 
All the solution between 0 and 2pi are pi/7, 5pi/7, pi, 9pi/7 and 13pi/7 only. 
 
One must consider the validity conversion of sin(x) term to cos in last step. It must remain valid for both the cases instead of only for cos cases. Hence half of general solution for cos will not be correct solutions. 
 
Validate yourself for so obtained solutions.

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More