Question

II. Answer any three of the following question
90 Prove that sin 2r+2sin 4x+sin 6x=4cos xsin 4r.
1.
Show that tan 3.x tan 2x tan x= tan 3r-tan 2r-tanx.
12.
sin 5x-2 sin 3r+sinx
Prove that
COS5r-cOSY
tany.
13.
Prove that cot 4x(sin 5x+sin 3x) = cotx(sin 5r-sin3
IV. Answer any one of the following questions​

Answer 1

Given : tan 3.x tan 2x tan x= tan 3x-tan 2x-tanx

To Find :  Prove that

Solution:

3x  = 2x + x

taking tan both sides

=> tan(3x) = tan (2x + x)

using tan (a + b)  = (tana + tanb)/(1 - tanatanb)

=> tan(3x)  = (tan2x + tanx)/(1 - tan2x.tanx)

=> tan3x -  tan3x.tan2x.tanx  = tan2x + tan  x

=>  -  tan3x.tan2x.tanx =  - tan3x + tan2x + tan  x

=>  tan3x.tan2x.tanx =  tan3x - tan2x - tan  x

QED

Hence proved

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