If and , then show that…

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If sin⁡α+sin⁡β=a\sin \alpha + \sin \beta = a and cos⁡α+cos⁡β=b\cos \alpha + \cos \beta = b , then show that tan⁡(α−β2)=±4−a2−b2a2+b2\tan\left(\frac{\alpha - \beta}{2}\right) = \pm \sqrt{\frac{4 - a^2 - b^2}{a^2 + b^2}} .

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