If and are the solutions of

MATHEMATICS · Multi correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If α\alpha and β\beta are the solutions of acos⁡θ+bsin⁡θ=ca\cos\theta+b\sin\theta=c, then (1) sin⁡α+sin⁡β=2bca2+b2\sin\alpha+\sin\beta=\frac{2bc}{a^2+b^2} (2) sin⁡αsin⁡β=c2−a2a2+b2\sin\alpha\sin\beta=\frac{c^2-a^2}{a^2+b^2} (3) sin⁡α+sin⁡β=2acb2+c2\sin\alpha+\sin\beta=\frac{2ac}{b^2+c^2} (4) sin⁡α+sin⁡β=ca2+b2\sin\alpha+\sin\beta=\frac{c}{a^2+b^2}

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