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

Mathematics

1 answer:

strojnjashka [21]3 years ago

8 0

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

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