Question

sin 60 .cos30-cos60 .sin30=1/2

Answer 1

L.H.S.

Sin60.cos30-cos60.sin30

Now we will put the values of the following trigonometrical ratios of standard angles.

Therefore,
Sin60°=√3/2
Cos30°=√3/2
Cos60°=1/2
Sin30°=1/2

Coming back to the equation of L.H.S.(with values)

$\frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} - \frac{1}{2} \times \frac{1}{2}$
$= \frac{3}{4} - \frac{1}{4}$

$= \frac{2}{4}$
$= \frac{1}{2}$
Which is R.H.S.

Hence,L.H.S=R.H.S
Therefore,

PROVED