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### Skills Section 2:

#### Problem 1:
Find all values of \( x \) between \( 0^\circ \leq x \leq 360^\circ \) such that:
- (i) \( \cos x = \cos 25^\circ \)
- (ii) \( \sin x = \sin 50^\circ \)

#### Problem 2:
Solve for \( 0^\circ \leq x \leq 360^\circ \):
- (i) \( \cos \left( x + \frac{3}{2} \right) = 2 \)
- (ii) \( \tan^2 x = 3 \)

#### Problem 3:
Solve the following equations for \( 0 \leq \theta \leq 2\pi \) giving your answers to 1 decimal place where necessary:
- (i) \( \cos \theta = 0.4 \)
- (ii) \( \tan \theta = -1.2 \)
- (iii) \( \sin^2 \theta = 1 \)

#### Problem 4:
Find values for \( x \) in the range \( 0 \leq \theta \leq \pi \):
- (i) \( 2 \sin x \cos x = \sin x \)

#### Problem 5:
Solve for \( x \), where \( -\pi \leq x \leq \pi \), giving your answer exactly where appropriate:
- (i) \( \cos 2x = \frac{\sqrt{3}}{2} \)
- (ii) \( \tan^2 x = \frac{1}{3} \)
- (iii) \( 2 \sin^2 x = \sin x + 1 \)

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Find all of the values of x between 0° to 360° such that: (i) cos x = cos 25° (ii) sin x = sin 50°. Solve for 0° ≤ x ≤ 360°: (i) cos (x + 3/2) = 2 (ii) tan^2 x = 3. Solve for 0 ≤ θ ≤ 2π: (i) cos θ = 0.4 (ii) tan θ = -1.2 (iii) sin^2 θ = 1. Find values for x in the range 0 ≤ θ ≤ π: (i) 2sin x cos x = sin x. Solve for x, where -π ≤ x ≤ π: (i) cos 2x = √3/2 (ii) tan^2 x = 1/3 (iii) 2sin^2 x = sin x + 1.

Solve trigonometric equations such as cos x = cos 25° and tan^2 x = 3 within the range 0° ≤ x ≤ 360°. Learn how to find multiple solutions and apply trigonometric identities to answer complex questions. Perfect for students in Grades 10-12.

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