Find the roots of the equation sin2x = √3cos2x belonging to the segment [-1; 6]

Dividing the equation by cos (2x) and using the definition of the tangent, we get the equation:

tg (2x) = 1;

2x = arctan (1) + – π * n, where n is a natural number;

x = π / 8 + – π / 2 * n.

Let’s solve the inequality:

-1 <π / 8 + – π / 2 * n <6;

-9π / 8 <+ – π / 2 * n <49π / 8;

-9/4 <+ – n <49/4;

n belongs to natural numbers from 1 to 12.