Solve: sin^2x + 2sinxcosx - 3cos^2x = 0?

Trigonometry is based on a picture of a circle with the radius making an angle with the x axis. You carry this picture in your head, not your calculator. Trig is mostly imagination and the rest memorization.

Remember Chief SohCahToa
Sin = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Also memorize:
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan

sin^2(x) + 2sin(x)cos(x) - 3cos^2(x) = 0

Substitute:
O^2/H^2 + 2OA/H^2 - 3A^2/H^2 = 0 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Multiply by H^2.

O^2 + 2OA - 3A^2 = 0 Only true when O = A therefore x = 45 degrees, 135 degrees, etc.