How do you solve sin(theta + pi/6) - cos (theta + pi/3) = sqrt3 * sin theta?

1 Answer
Nghi N.
Apr 4, 2016

Prove trig expression

Explanation:

Apply the 2 trig identities:
sin (a + b) = sin a.cos b + sin b.cos a
cos (a + b) = cos a.cos b - sin a.sin b
sin (t + pi/6) = sin t.cos (pi/6) + sin (pi/6).cos t =
= (sqrt3/2).sin t + (cos t)/2 (1)
cos (t + pi/3) = cos (t).cos (pi/3) - sin (pi/3).sin t =
= cos (t/2) - (sqrt3/2).sin t. (2)
Subtract (2) from (1), we get:
2(sqrt3/2).sin t = sqrt3.sin t

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
12023 views around the world
You can reuse this answer
Creative Commons License