Popular >

sin(4x)=-sin(2x)

Solution

sin (4 x) = - sin (2 x)

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

Solution steps

sin (4 x) = - sin (2 x)

Subtract

- sin (2 x)

from both sides

sin (4 x) + sin (2 x) = 0

Rewrite using trig identities

2 cos (x) sin (3 x) = 0

Solving each part separately

cos (x) = 0 or sin (3 x) = 0

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

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

Combine all the solutions

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

t, x = 1 - 2 cos (2 t)

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

cos (x) = 0.587

\frac{sec ( x ) + csc ( x )}{1 + tan ( x )} = sin (x)

sec (x) - \frac{sin ( x )}{cos ( x )} = cos (x)