Solve the equation

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the equation cos⁡(2θ+45∘)=−22\cos\bigl(2\theta + 45^{\circ}\bigr)= -\dfrac{\sqrt{2}}{2}, where θ\theta is measured in degrees. (i) Obtain the general solution for θ\theta. (ii) Write all values of θ\theta that satisfy the equation in the interval −180∘≤θ<180∘-180^{\circ} \le \theta < 180^{\circ}.

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