Question

Prove that Sin 60° cos 30° – cos 60° sin 30° = sin 30

Answer 1

Answer:

Sin 60° cos 30° – cos 60° sin 30° = sin 30

Answer 2

$\large\underline{\sf{Solution}}$

$\mathrm{sin60° \:cos 30° - cos 60° \: sin 30°=sin30°}$

$\mathrm{=\large (\frac{ \sqrt{3} }{2}) \times ( \frac{ \sqrt{3} }{2}) - ( \frac{1}{2} ) \times ( \frac{1}{2} ) = \frac{1}{2} }$

$\mathrm{= > \large\frac{3}{4} - \frac{1}{4} = \frac{1}{2} }$

$\mathrm{ = > \large \frac{3 - 1}{4} = \frac{1}{2} }$

$\mathrm{ = > \large \frac{2}{4} = \frac{1}{2} }$

$\mathrm{\therefore \frac{1} {2} =\frac{1} {2}}$

LHS = RHS

Hence, proved.