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Prove the following:

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Prove the following:

(a) \(\cos (\alpha+\beta)+\cos (\alpha-\beta)=2 \cos \alpha \cdot \cos \beta\)
(b) \(\sin \left(\theta+30^{\circ}\right)-\sin \left(\theta-30^{\circ}\right)=\cos \theta\)
(c) \(\cos \left(45^{\circ}-\theta\right)-\sin \left(45^{\circ}-\theta\right)=\sqrt{2} \sin \theta\)
(d) \(\sqrt{3} \sin \left(\theta+60^{\circ}\right)-\sin \left(\theta+30^{\circ}\right)=\cos \theta\)
(e) \(\sin \left(\mathrm{A}-60^{\circ}\right)+\cos \left(\mathrm{A}-30^{\circ}\right)=\sin \mathrm{A}\)
in Mathematics by ♦ Diamond (75,025 points) | 9 views

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