Home
Class 11
MATHS
Prove that: \ s in3x+s in2x-s in x=4s in...

Prove that: `\ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2`

Text Solution

Verified by Experts

We know that,
`sinx−siny=2cos((x+y​)/2)sin((x−y​)/2)`
putting `x=2x` and ` y=x`
`=>2cos((3x+x​)/2)sin((3x−x​)/2)`
`=>2cos((4x)/2)sin((2x​)/2)`
`=>sin3x+(sin2x−sinx)`
`=>sin3x+[2cos((3x)/2​)sin(x/2​)]->(1)`
We know that
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Prove that: s in3A+s in2A-s in A=4s in A(cos A)/(2)(cos A)/(2)cos3(A)/(2)(cos(3A))/(2)

Prove that: sin^(2)6x-sin^(2)4x=s in2xs in10x

Prove that: (s in5x-2s in3x+s in x)/(cos5x-cos x)=tan x

Prove that: cos^(2)2x-cos^(2)6x=s in4xs in8x

Prove that: (cos9x-cos5x)/(s in17x-s in3x)=-(s in2x)/(cos10x)

Prove that: s in x+s in3x++sin(2n-1)x=(sin^(2)nx)/(s in x) for all n in N.

The number of distinct real roots of the equation |cosx s in x s in x s in x cos x s in x s in x s in x cos x|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

Solve the equation sin^(4)x+cos^(4)x=(7)/(2)s in x cos x

Evaluate: int_0^(pi//2)(s in x-cosx)/(1+s in xcosx)dx

Prove that: (cos4A+cos3A_(cos2A))/(s in4A+s in3A+si2 A)=cot3A

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: cot^2A-tan^2A=4 cot2A cosec2A

    Text Solution

    |

  2. sin4A=4sinAcos^3A-4cosAsin^3A

    Text Solution

    |

  3. Prove that: \ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2

    Text Solution

    |

  4. If cos x=\ -3/5a n d\ x lies in the IIIrd quadrant, find the values of...

    Text Solution

    |

  5. If cos x=-3/5a n d\ x lies in IIInd quadrant, find the values of sin2x...

    Text Solution

    |

  6. If sinx=(sqrt(5))/3a n d\ x lies in IInd quadrant, find the values of ...

    Text Solution

    |

  7. Prove that 1+cos^2 2x=2(cos^4x+sin^4x)

    Text Solution

    |

  8. If costheta=4/5 and theta is acute, find the tan2theta

    Text Solution

    |

  9. If sinx=4/5 and 0ltxltpi/ 2, find the value of sin4x

    Text Solution

    |

  10. Prove that: \ cos7^0cos 14^0cos 28^0cos 56^0=(s in 68^0)/(16cos83^0)

    Text Solution

    |

  11. Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

    Text Solution

    |

  12. cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)=1/16

    Text Solution

    |

  13. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

    Text Solution

    |

  14. sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

    Text Solution

    |

  15. If sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that: cos(alpha-bet...

    Text Solution

    |

  16. If costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ prove that tanth...

    Text Solution

    |

  17. If sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta, prove that costhet...

    Text Solution

    |

  18. If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)=56/65

    Text Solution

    |

  19. Prove that: 8cos^3pi/9-\ 6cospi/9=1.

    Text Solution

    |

  20. Prove that: 108sinpi/(18)-144sin^3pi/(18)=18

    Text Solution

    |