For two angles and the following information is given: with

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

For two angles α\alpha and β\beta the following information is given: sin⁡α=45\sin \alpha=\dfrac45 with 90∘<α<180∘90^\circ<\alpha<180^\circ, and cos⁡β=513\cos \beta=\dfrac{5}{13} with 270∘<β<360∘270^\circ<\beta<360^\circ. Using these data, find the exact values of: (i) cos⁡α\cos \alpha and sin⁡β\sin \beta (ii) sin⁡(α+β)\sin(\alpha+\beta) (iii) cos⁡(α−β)\cos(\alpha-\beta) (iv) tan⁡(α+β)\tan(\alpha+\beta)

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