निम्नलिखित को सिद्ध कीजिए
$\cot 4 x(\sin 5 x+\sin 3 x)=\cot x(\sin 5 x-\sin 3 x)$
निम्नलिखित को सिद्ध कीजिए
$\cot 4 x(\sin 5 x+\sin 3 x)=\cot x(\sin 5 x-\sin 3 x)$
$L.H.S$ $=\cot 4 x(\sin 5 x+\sin 3 x)$
$=\frac{\cot 4 x}{\sin 4 x}\left[2 \sin \left(\frac{5 x+3 x}{2}\right) \cos \left(\frac{5 x-3 x}{2}\right)\right]$
$\left[\because \sin A+\sin B=2 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\right]$
$=\left(\frac{\cos 4 x}{\sin 4 x}\right)[2 \sin 4 x \cos x]$
$=2 \cos 4 x \cos x$
$R.H.S.$ $=\cot x(\sin 5 x-\sin 3 x)$
$=\frac{\cos x}{\sin x}\left[2 \cos \left(\frac{5 x+3 x}{2}\right) \sin \left(\frac{5 x-3 x}{2}\right)\right]$
$\left[\because \sin A-\sin B=2 \cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\right]$
$=\frac{\cos x}{\sin x}[2 \cos 4 x \sin x]$
$=2 \cos 4 x \cdot \cos x$
$L.H.S.$ $=$ $R.H.S.$
Similar Questions
यदि $A = 133^\circ ,$ तब $\;2\cos \frac{A}{2} =$
यदि $A = 133^\circ ,$ तब $\;2\cos \frac{A}{2} =$
यदि $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ तब $x = $
यदि $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ तब $x = $
यदि $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right)$ , तब $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ बराबर है
यदि $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right)$ , तब $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ बराबर है
- [IIT 1984]
$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $
$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $
यदि $\sin \alpha = \frac{{336}}{{625}}$ तथा $450^\circ < \alpha < 540^\circ ,$ हो तो $\sin \left( {\frac{\alpha }{4}} \right) $ बराबर है
यदि $\sin \alpha = \frac{{336}}{{625}}$ तथा $450^\circ < \alpha < 540^\circ ,$ हो तो $\sin \left( {\frac{\alpha }{4}} \right) $ बराबर है