Trigonometric Equations Reducible to Quadratic for Math Skills

Trigonometric Equations Reducible to Quadratic for Math Skills are based on trigonometric identities such as;
$$\sin^2{x} + \cos^2{x} = 1 \\ 1 + \cot^2{x} = \csc^2{x} \\ \tan^2{x} + 1 = \sec^2{x} \\$$

Practice Questions

Question 1

Solve $2 \cos^2{x} – 3 \cos{x} + 1 = 0$ for $0^\circ \ge x \ge 360^\circ$.

Question 2

Solve $\sec^2{x} + 2 \tan{x} = 0$ for $0^\circ \ge x \ge 360^\circ$.

Question 3

Solve $\cot^2{x} = \csc{x} + 1$ for $0^\circ \ge x \ge 360^\circ$.

Question 4

Solve $\cos^2{x} + \cos{x} = \sin^2{x}$ for $0^\circ \ge x \ge 360^\circ$.