Question

solve 3tan((theta)-15)=tan((theta) +15)

Answer 1

Answer:

The value of $\theta=45$          

Step-by-step explanation:

Given : Expression  $3\tan(\theta-15)=\tan(\theta+15)$    

To find : Solve the expression?

Solution :

Expression $3\tan(\theta-15)=\tan(\theta+15)$    

$3=\frac{\tan(\theta+15)}{\tan(\theta-15)}$    

Apply Componendo & Dividendo  used to reduce the number of expansions needed.

i.e. $\frac{(p+q)}{(p-q)}=\frac{(r+s)}{(r-s)}$

$\frac{3+1}{3-1}=\frac{\tan(\theta+15)+\tan(\theta-15)}{\tan(\theta+15)-\tan(\theta-15)}$                              

$2=\frac{\frac{\sin(\theta+15)}{\cos(\theta+15)}+\frac{\sin(\theta-15)}{\cos(\theta-15)}}{\frac{\sin(\theta+15)}{\cos(\theta+15)}-\frac{\sin(\theta-15)}{\cos(\theta-15)}}$                      

$2=\frac{\frac{\sin(\theta+15)\cos(\theta-15)+\sin(\theta-15)\cos(\theta+15)}{\cos(\theta+15)\cos(\theta-15)}}{\frac{\sin(\theta+15)\cos(\theta-15)-\sin(\theta-15)\cos(\theta+15)}{\cos(\theta+15)\cos{\theta-15}}}$

$2=\frac{\sin(\theta+15+\theta-15)}{\sin(\theta+15-\theta+15)}$

$2=\frac{\sin(2\theta)}{\sin(30)}$

$2\times \sin 30=\sin(2\theta)$

$2\times \frac{1}{2}=\sin(2\theta)$

$\sin(2\theta)=1$

$\sin(2\theta)=\sin 90$

$2\theta=90$

$\theta=45$

Therefore, The value of $\theta=45$

Answer 2

Here is the solution.

Answer is

$n\pi + \frac{\pi}{4}$