(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) sin4 x = sin2 x Solution
(ii) 2 cos2 x + 1 = −3 cos x Solution
(iii) 2 sin2 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 cos2 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
Solution
(x) cos 2θ = (√5 + 1)/4 Solution
(xi) 2 cos2 x − 7 cos x + 3 = 0 Solution
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