A quadratic trigonometric equation is any equation with a 
or
term, or a
or
term, since these become quadratic on using the appropriate double angle identity.
The solutions of trigonometric equations can be found by factorisation or using the quadratic formula. Generally the roots are required in an interval of 360 ° - either [0 °, 360 °] or [-180 °, 180 °] .
Example: Solve the equation
for the range 0 ° - 360 °.
Use the identity
to obtain
This equation factorises to give
Now put each factor equal to 0 and solve.
Exaple: Solve the equation cos 2x = sin x in the interval [-180 °, 180 °] .
Use the identity
to obtain
Move all the terms to one side to obtain
This expression factorises as
Put each factor equal to 0 and solve.
