Ask Questions, Get Answers

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

If $\cos\theta=\large\frac{\cos\alpha-\cos\beta}{1-\cos\alpha\cos\beta}$ then prove that one of the values of $\tan\large\frac{\theta}{2}$ is $\tan \large\frac{\alpha}{2}$$\cot \large\frac{\beta}{2}$

Can you answer this question?

2 Answers

0 votes
Tan thita/2= tan@/2 cot bits /2
answered Feb 23 by nehanagwani
Cot bits /2 = tan bits /2 ?????
–1 vote
  • $\tan\large\frac{\theta}{2}=\frac{1-\cos \theta}{\sin \theta}$
$\tan\large\frac{\theta}{2}=\frac{(1-\cos \theta)^2}{\sin^2 \theta}$
$\Rightarrow \large\frac{(1-\cos \theta)^2}{1-\cos^2\theta}$
$\Rightarrow \large\frac{1-\cos \theta}{1+\cos \theta}$
$\Rightarrow \large\frac{1-\Large\frac{\cos \alpha-\cos \beta}{1-\cos \alpha\cos\beta}}{1+\Large\frac{\cos \alpha-\cos \beta}{1-\cos \alpha\cos\beta}}$
$\Rightarrow \large\frac{1-\cos \alpha\cos\beta-\cos \alpha+\cos \beta}{1-\cos \alpha\cos \beta+\cos \alpha-\cos\beta}$
$\Rightarrow \large\frac{(1-\cos \alpha)+\cos\beta(1-\cos \alpha}{(1+\cos \alpha)-\cos \beta(1+\cos \alpha)}$
$\Rightarrow \large\frac{(1-\cos \alpha)(1+\cos \beta)}{(1+\cos \alpha)(1-\cos \beta)}$
$\Rightarrow \tan^2\large\frac{\alpha}{2}$$\cot^2\large\frac{\beta}{2}$
$\therefore \tan \large\frac{\theta}{2}=$$\pm \tan \large\frac{\alpha}{2}$$\tan\large\frac{ \beta}{2}$
Hence one of the values of $\tan\large\frac{\theta}{2}$ is $\tan \large\frac{\alpha}{2}$$\tan \large\frac{\beta}{2}$
Hence proved
answered May 22, 2014 by sreemathi.v
Pls tell me how is this possible
Hence one of the values of tanθ2tanθ2 is tanα2tanα2tanβ2tanβ2
Hence proved

Related questions

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