Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
Answer
Comment
Share
Q)

If $3\tan \theta\tan\phi=1$ ,prove that $2\cos (\theta+\phi)=\cos (\theta-\phi)$

1 Answer

Comment
A)
Toolbox:
  • $\cot\theta=\large\frac{\cos \theta}{\sin \theta}$
  • $\cos(\theta+\phi)=\cos \theta\cos\phi-\sin \theta\sin \phi$
  • $\cos(\theta-\phi)=\cos \theta\cos\phi+\sin \theta\sin \phi$
Given :
$3\tan \theta\tan\phi=1$ or $\cot \theta\cot\phi=3$
Or $\large\frac{\cos \theta.\cos \phi}{\sin \theta.\sin \phi}=\frac{3}{3}$
By componendo or dividendo,we have
$\large\frac{\cos \theta.\cos \phi+\sin\theta\sin\phi}{\cos\theta\cos\phi-\sin \theta.\sin \phi}=\frac{3+1}{3-1}$
$\large\frac{\cos(\theta-\phi)}{\cos(\theta+\phi)}$$=2$
$2\cos (\theta+\phi)=\cos (\theta-\phi)$
Hence proved
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...