frac{sin A+sin 7 A+sin 13 A}{cos A+cos 7 A+co | vedclass

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Question

(C) Given expression: $\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A}$ Group the terms with $A$ and $13A$: $= \frac{(\sin 13 A+\sin A)+\s

Vedclass · Accepted Answer

$	an 7 A$

Vedclass · Answer

(C) Given expression: $\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A}$ Group the terms with $A$ and $13A$: $= \frac{(\sin 13 A+\sin A)+\sin 7 A}{(\cos 13 A+\cos A)+\cos 7 A}$ Using sum-to-product formulas $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$ and $\cos C + \cos D = 2 \cos(\frac{C+D}{2}) \cos(\frac{C-D}{2})$: $= \frac{2 \sin(\frac{13A+A}{2}) \cos(\frac{13A-A}{2}) + \sin 7 A}{2 \cos(\frac{13A+A}{2}) \cos(\frac{13A-A}{2}) + \cos 7 A}$ $= \frac{2 \sin 7 A \cos 6 A + \sin 7 A}{2 \cos 7 A \cos 6 A + \cos 7 A}$ Factor out $\sin 7 A$ from the numerator and $\cos 7 A$ from the denominator: $= \frac{\sin 7 A(2 \cos 6 A + 1)}{\cos 7 A(2 \cos 6 A + 1)}$ $= \frac{\sin 7 A}{\cos 7 A} = 	an 7 A$

$\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A} =$

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