Trigonometry> Prove that: tan5x+tan3x/tan5x-tan3x=4cos2...

Prove that: tan5x+tan3x/tan5x-tan3x=4cos2xcos4x

Kartik Sawant , 10 Years ago

Grade 12

3 Answers

Latika Leekha

Last Activity: 10 Years ago

Hello student,
We first consider the L.H.S. and try to reach the R.H.S.
L.H.S = $\frac{tan 5x + tan 3x}{tan 5x - tan 3x}$
= $\frac{\frac{sin 5x}{cos 5x}+\frac{sin 3x}{cos 3x}}{\frac{sin 5x}{cos 5x}-\frac{sin 3x}{cos 3x}}$
= $\frac{sin 5x cos 3x +sin 3x cos 5x}{sin 5x cos 3x - sin 3x cos 5x}$
= $\frac{sin (5x+3x)}{sin (5x-3x)}$
(Using the formula sin A cos B + cos A sin B = sin (A+B) )
= $\frac{sin 8x}{sin 2x}$
= 2 sin 4x cos 4x/sin 2x
= 2(2 sin 2x cos 2x)cos 4x/sin 2x
= 4 cos 2x cos 4x.
= R.H.

Sai Sampath

Last Activity: 10 Years ago

= $\frac{sin 5x cos 3x +sin 3x cos 5x}{sin 5x cos 3x - sin 3x cos 5x}$ = $\frac{\frac{sin 5x}{cos 5x}+\frac{sin 3x}{cos 3x}}{\frac{sin 5x}{cos 5x}-\frac{sin 3x}{cos 3x}}$ = $\frac{tan 5x + tan 3x}{tan 5x - tan 3x}$ (Using the formula sin A cos B + cos A sin B = sin (A+B)

$\frac{sin (5x+3x)}{sin (5x-3x)}$

= 2 sin 4x cos 4x/sin 2x= 2(2 sin 2x cos 2x)cos 4x/sin 2x= 4 cos 2x cos 4x. $\frac{sin 8x}{sin 2x}$

Om

Last Activity: 3 Years ago

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nice solution of latika madam