**Solving Trigonometric Equations Worksheet :**

Here we are going to see some practice questions on solving trigonometric equations.

(1) Find the principal solution and general solutions of the following:

(i) sin θ = −1/√2

**(ii) **cot θ = √3

**(iii) tan** θ = -1/√3 Solution

(2) Solve the following equations for which solutions lies in the interval 0° ≤ θ < 360°

(i) sin^{4} x = sin^{2} x Solution

(ii) 2 cos^{2} x + 1 = −3 cos x Solution

(iii) 2 sin^{2} x+1 = 3sinx Solution

(iv) cos 2x = 1 - 3 sin x Solution

(3) Solve the following equations:

(i) sin 5x − sin x = cos3x Solution

(ii) 2 cos^{2} θ + 3sinθ − 3 = 0 Solution

(iii) cos θ + cos3θ = 2cos2θ Solution

(iv) sin θ + sin3θ + sin5θ = 0 Solution

(v) sin 2θ − cos 2θ − sin θ + cos θ = 0 Solution

(vi) sin θ + cos θ = √2 Solution

(vi) sin θ + cos θ = √2 Solution

(vii) sin θ + √3 cos θ = 1 Solution

(viii) cot θ + cosecθ = √3 Solution

(ix) tan θ + tan (θ + π/3) + tan (θ + 2π/3) = √3

(x) cos 2θ = (√5 + 1)/4 Solution

(xi) 2 cos^{2} x − 7 cos x + 3 = 0 Solution

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