Home
Class 11
MATHS
Prove that: \ sin3x+sin2x-sin x=4sin xco...

Prove that: `\ sin3x+sin2x-sin x=4sin xcos(x/2)cos((3x)/2)`

Text Solution

Verified by Experts

LHS `=sin3x+sin2x-sinx`
`=sin3x+2cos(2x+x)/(2)sin(2x-x)/(2)`
`=2sin(3x)/(2)cos(3x)/(2)+2cos(3x)/(2)sinx/2`
`=2cos(3x)/(2) [ sin(3x)/(2)+sinx/2]`
`=2cos(3x)/(2)[2sin((3x)/(2)+x/2)sin(2x-x)/(2)]`
`=2cos(3x)/(2)[sin(3x)/(2)+sinx/2]`
`=2cos(3x)(2)[2sin(2x)/(2)cosx/2]`
`=2cos(3x)/(2)[2sinxcosx/2]`
`=4sinxcosx/2cos(3x)/(2)`= RHS Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3.4|8 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos

Similar Questions

Explore conceptually related problems

sin x sin 2x sin 3x

Prove that: sin 3x + sin 2x - sin x = 4 sin x cos x/2 cos (3x)/2

int sin x sin2x sin3x

Prove that: sin2x+2sin4x+sin6x=4cos^2xsin4

Prove that : sin x+sin3x+sin5x+sin7x=4cos x\ cos2xsin4x

Prove that sinx + sin3x + sin5x+ sin7x=4cosxcos2xsin4x

prove that sin2x+2sin4x+sin6x=4cos^(2)x.sinx

Prove that: (sin 3 x +sin x) sin x + (cos 3x - cos x) cos x = 0

Solve 4 sin x sin 2x sin 4x = sin 3x .

Prove that: (sin5x-2sin3x+sin x)/(cos5x-cos x)=tanx