Question

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

Answer 1

see explanation

Explanation:

left side = sin300° = - sin60° and sin60 =
`(√(3) )/(2)`, thus

sin300° = -
`(√(3) )/(2)`

right side

sin150° = sin30° =
`(1)/(2)` and

cos150° = - cos30° = -
`(√(3) )/(2)`, thus

2sin150°cos150°

= 2 ×
`(1)/(2)` × -
`(√(3) )/(2)` = -
`(√(3) )/(2)`

left side = right side ⇒ True