solvefor x,sin(x)-sin(2x)=0

Solution

solve for

x, sin (x) - sin (2 x) = 0

x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

Solution steps

sin (x) - sin (2 x) = 0

Rewrite using trig identities

- 2 cos (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

cos (\frac{3 x}{2}) = 0 or sin (\frac{x}{2}) = 0

cos (\frac{3 x}{2}) = 0 : x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}

sin (\frac{x}{2}) = 0 : x = 4 πn, x = 2 π + 4 πn

Combine all the solutions

x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

sin (θ) = \frac{4}{5}, cos (θ)

sin (6 x) = cos (3 x)

sin (\frac{θ}{2}) - cos (\frac{θ}{2}) = 0

sin (x) = \frac{- 3}{5}

3 cos^{2} (a) + sin^{2} (a) = 2