Home
Class 12
MATHS
Prove that: (cos7x-cos8x)/(1+2cos5x)=cos...

Prove that: `(cos7x-cos8x)/(1+2cos5x)=cos2x-cos3x`

Text Solution

Verified by Experts

We have , `int(cos7x-cos8x)/(1+2cos5x)dx=1/2int(2sin(5x)/(2)cos7x-2sin(5x)/(2)cos8x)/(sin(5x)/(2)+2cos5xsin(5x)/(2))dx`
`1/2intsin(19x)/(2)-sin(9x)/(2)-(sin(21x)/(2)-sin(11x)/(2))/(sin(5x)/(2)+sin(15x)/(2)-sin(5x)/(2))dx`
`1/2int((sin(19x)/(2)+sin(11x)/(2)-(sin(21x)/(2)+sin(9x)/(2)))/(sin(15x)/(2)+sin(15x)/(2)-sin(5x)/(2)))dx`
`1/2int((sin(19x)/(2)+sin(11x)/(2))-(sin(21x)/(2)+sin(9x)/(2)))/(sin(15x)/(2))dx`
`1/2int(2sin(15x)/(2)cos2x-2sin(15x)/(2)cos3x)/(sin(15x)/(2))dx=int(cos2x-cos3x)dx=1/2sin2x-1/3sin3x+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise EXERCISE -1 SUBJECTIVE QUESTIONS|1 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SUBJECTIVE QUESTIONS|14 Videos

  • FUNDAMENTAL OF MATHEMATICS

    RESONANCE ENGLISH|Exercise Exercise|135 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos

Similar Questions

Explore conceptually related problems

To prove (cos5x+cos4x)/(1-2cos3x) = -cos2x-cosx

int(cos7x-cos8x)/(cos2x-cos3x)dx

Prove that (cos7x+cos5x)/(sin7x-sin5x)=cotx .

Prove that: 1+cos2x+cos4x+cos6x=4cosxcos2xcos3x

Prove that: (cos9x-cos5x)/(sin17 x-sin3x)=-(sin2x)/(cos10 x)

Prove that 2cosx. Cos 3x- 2cos 5x. Cos 7x- cos 4x + cos12x=0 .

Prove that: (cos9x-cos5x)/(sin 17 x-sin3x)=\ -(sin2x)/(cos 10 x)

Prove that: cos6x=32cos^6x-48cos^4x+18cos^2x-1

The value of the integral int(cos7x-cos8x)/(1+2cos5x)dx can be

Prove that: (sin5x+sin3x)/(cos5x+cos3x)=tan4x