Let and be function defined by and

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let ff and gg be function defined by f(θ)=cos⁡2θf(\theta) = \cos^2 \theta and g(θ)=tan⁡2θg(\theta) = \tan^2 \theta, suppose α\alpha and β\beta satisfy 2f(α)−g(β)=12f(\alpha) - g(\beta) = 1, then value of 2f(β)−g(α)2f(\beta) - g(\alpha) is

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