Question

Find the value of $x$, if $\tan 3x=\sin 45.\cos 45+\sin 30$.

Answer 1

R.H.S

$\sin 45\cdot \cos {45}^o+\sin 30$

$=\frac{1}{\sqrt{2}}.\frac{1}{\sqrt{2}}+\frac{1}{2}$

$=\frac{1}{2}+\frac{1}{2}$

$=\frac{2}{2}$

$=1$

Now,

L.H.S

$\tan 3x=1$

But $\tan {45}^o=1$

$\therefore \tan 3x=\tan 45$

$\Rightarrow 3x=45$

$\Rightarrow x=\frac{45}{3}$

$\therefore x=15$.