Question

prove that (sin 35 cos55+cos 35 sin 55)+ root3 (tan 10 tan 30 tan80)=2

Answer 1

Solution-

The given expression is,

$=(\sin 35.\cos55+\cos 35.\sin 55)+ \sqrt 3(\tan 10.\tan 30.\tan 80)$

We know,

$\sin(A+B)=\sin A.\cos B+\cos A.\sin B\ and\ \tan (90-x)=\cot x$

Applying so,

$=(\sin (35+55))+ \sqrt 3(\tan 10.\tan 30.\cot 10)$

We also know that,

$\tan x\times \cot x=1$

$=(\sin 90)+ \sqrt 3(\tan 30.1)$

$=1+ \sqrt 3(\frac{1}{\sqrt{3}})$

$=1+ 1$

$=2$ (proved)