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Questions  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Q)

Prove $\large\frac{\cos 4x+\cos 3x+\cos 2x}{\sin 4x+\sin 3x+\sin 2x}$$=\cot 3x$

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  • $\cos x+\cos y=2\cos \large\frac{x+y}{2}$$.\cos \large\frac{x-y}{2}$
  • $\sin x+\sin y=2\sin \Large\frac{x+y}{2}$$\cos\large\frac{x-y}{2}$
L.H.S
$\large\frac{\cos 4x+\cos 3x+\cos 2x}{\sin 4x+\sin 3x+\sin 2x}$
$\Rightarrow \large\frac{\cos 4x+\cos 2x+\cos 3x}{\sin 4x+\sin 2x+\sin 3x}$
$\Rightarrow \large\frac{2\cos \Large\frac{4x+2x}{2}.\cos \Large\frac{4x-2x}{2}\normalsize +\cos 3x}{2\sin \Large\frac{4x+2x}{2}.\cos \Large\frac{4x-2x}{2}\normalsize +\sin 3x}$
$\Rightarrow \large\frac{2\cos 3x.\cos x+\cos 3x}{2\sin 3x.\cos x+\sin 3x}$
$\Rightarrow \large\frac{\cos 3x(2\cos x+1)}{\sin 3x(2\cos x+1)}$
$\Rightarrow \large\frac{\cos 3x}{\sin 3x}$
$\Rightarrow \cot 3x$=R.H.S
Hence proved.
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