logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
0 votes

Prove that $\large\frac{(\sin 7x+\sin 5x)+(\sin 9x+\sin 3x)}{(\cos 7x+\cos 5x)+(\cos 9x+\cos 3x)}$$=\tan 6x$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $\sin A+\sin B=2\sin \large\frac{A+B}{2}$$\cos \large\frac{A-B}{2}$
  • $\cos A+\cos B=2\cos \large\frac{A+B}{2}$$\cos \large\frac{A-B}{2}$
L.H.S
$\large\frac{(\sin 7x+\sin 5x)+(\sin 9x+\sin 3x)}{(\cos 7x+\cos 5x)+(\cos 9x+\cos 3x)}$
$\large\frac{2\sin\Large\frac{7x+5x}{2}\normalsize \cos\Large\frac{7x-5x}{2}\normalsize +2\sin\Large\frac{9x+3x}{2}\normalsize\cos\Large\frac{9x-5x}{2}}{2\cos\Large\frac{7x+5x}{2}\normalsize \cos\Large\frac{7x-5x}{2}\normalsize +2\cos\Large\frac{9x+3x}{2}\normalsize\cos\Large\frac{9x-5x}{2}}$
$\large\frac{2\sin 6x\cos x+2\sin 6x\cos 3x}{2\cos 6x\cos x+2\cos 6x\cos 3x}$
$\large\frac{\sin 6x(\cos x+\cos 3x)}{\cos 6x(\cos x+\cos 3x)}$
$\large\frac{\sin 6x}{\cos 6x}$
$\tan 6x$=R.H.S
Hence proved.
answered Apr 18, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...