frac{sin 3theta + sin 5theta + sin 7theta + s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given expression: $\frac{\sin 3	heta + \sin 5	heta + \sin 7	heta + \sin 9	heta}{\cos 3	heta + \cos 5	heta + \cos 7	heta + \cos 9	heta}$ Gr

Vedclass · Accepted Answer

$	an 6	heta$

Vedclass · Answer

(C) Given expression: $\frac{\sin 3	heta + \sin 5	heta + \sin 7	heta + \sin 9	heta}{\cos 3	heta + \cos 5	heta + \cos 7	heta + \cos 9	heta}$ Group the terms: $\frac{(\sin 9	heta + \sin 3	heta) + (\sin 7	heta + \sin 5	heta)}{(\cos 9	heta + \cos 3	heta) + (\cos 7	heta + \cos 5	heta)}$ Using the sum-to-product formulas $\sin A + \sin B = 2 \sin \frac{A+B}{2} \cos \frac{A-B}{2}$ and $\cos A + \cos B = 2 \cos \frac{A+B}{2} \cos \frac{A-B}{2}$: Numerator: $2 \sin 6	heta \cos 3	heta + 2 \sin 6	heta \cos 	heta = 2 \sin 6	heta (\cos 3	heta + \cos 	heta)$ Denominator: $2 \cos 6	heta \cos 3	heta + 2 \cos 6	heta \cos 	heta = 2 \cos 6	heta (\cos 3	heta + \cos 	heta)$ Dividing the numerator by the denominator: $\frac{2 \sin 6	heta (\cos 3	heta + \cos 	heta)}{2 \cos 6	heta (\cos 3	heta + \cos 	heta)} = \frac{\sin 6	heta}{\cos 6	heta} = 	an 6	heta$.

$\frac{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta}{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta} = $

Similar Questions

If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$ and $0 \leq \alpha \leq \frac{\pi}{2}$,then the value of $\cos 2 \theta$ is

$\tan 75^\circ - \cot 75^\circ = $

The value of $\sin 47^\circ + \sin 61^\circ - \sin 11^\circ - \sin 25^\circ = $

If $0 < A < B < \frac{\pi}{4}$,$\cos (A+B) = \frac{11}{61}$ and $\sin (A-B) = \frac{24}{25}$,then $\sin 2A + \sin 2B = $

If $\cos (A - B) = \frac{3}{5}$ and $\tan A \tan B = 2$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module