Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove the following sin(2x) + 2sin(4x) + sin(6x) = 4cos^2(x)sin(4x)

Q (14) Prove the following

\small \sin2x +2\sin4x + \sin6x = 4\cos^{2}x\sin4x

Answers (1)

We know that 

\sin A+ \sin B = 2\sin \left ( \frac{A+B}{2} \right )\cos\left ( \frac{A-B}{2} \right )
We are using this identity 
sin2x + 2sin4x + sin6x = (sin2x + sin6x) + 2sin4x 

sin2x + sin6x = 2sin4xcos(-2x) =  2sin4xcos(2x)          (\because cos(-x) = cos x)

So, our equation becomes
sin2x + 2sin4x + sin6x = 2sin4xcos(2x) + 2sin4x
Now, take the 2sin4x common
sin2x + 2sin4x + sin6x = 2sin4x(cos2x +1)           (  \because \cos2x = 2\cos^{2}x - 1 )
                                     =2sin4x(2\cos^{2}x - 1 +1 )
                                     =2sin4x(2\cos^{2}x)
                                     =4\sin4x\cos^{2}x
                                                                          R.H.S.

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question