Question

Sin 300° = 2 sin 150° cos 150° use exact values to show it is true​

Answer 1

Answer:

see explanation

Step-by-step explanation:

left side = sin300° = - sin60°  and sin60 = $\frac{\sqrt{3} }{2}$, thus

sin300° = - $\frac{\sqrt{3} }{2}$

right side

sin150° = sin30° = $\frac{1}{2}$ and

cos150° = - cos30° = - $\frac{\sqrt{3} }{2}$, thus

2sin150°cos150°

= 2 × $\frac{1}{2}$ × - $\frac{\sqrt{3} }{2}$ = - $\frac{\sqrt{3} }{2}$

left side = right side ⇒ True