Question

If sin 2x = sin 60 cos 30° -cos 60° sin 30°, find the value of x.​

Answer 1

Answer:

Step-by-step explanation:

sin 2x = sin 60 cos 30° -cos 60° sin 30°

sin 2x = (root 3)/2 *(root 3)/2 - 1/2 * 1/2

sin 2x = 3/4 - 1/4

sin 2x=2/4

sin 2x=1/2

Since sin 30°=1/2 therefore 2x=30°

                                                  x=15°

Answer 2

Here we use a compound angle formula:

sin (A - B) = sin A · cos B - cos A · sin B

Here we take,

A = 60°

B = 30°

Thus,

sin (60° - 30°) = sin 60° · cos 30° - cos 60° · sin 30°

Putting LHS of  sin (2x) = sin 60 cos 30° -cos 60°  to the RHS of this equation,

sin (60° - 30°) = sin (2x)

sin 30° = sin (2x)

From both sides,

2x = 30°

x = 15°

Hence 15° is the answer.