Home
Class 12
MATHS
Prove that (cos^3x - sin^3x)/(cosx - sin...

Prove that `(cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|20 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 7|7 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 6|5 Videos

Similar Questions

Explore conceptually related problems

Prove that (sinx - sin3x)/(cos^2x - sin^2x) = -2sinx

Prove that (2cos^3x-cosx)/(sinx - 2sin^3x) = cotx

Prove that : (cos 9x - cos 5x)/(sin 17x -sin 3x)=- (sin 2x)/(cos 10x) .

Prove that (sin17x - sin3x)/(cos9x - cos5x) = -(cos10x)/(sin2x)

Prove that (cos5x + cos3x)/(sin5x + sin3x) = cot4x

Prove that (cos5x - cosx)/(sin5x - 2sin3x + sinx) = cotx

Prove that: (sinx +sin3x)/(cosx+cos3x)=tan2x

Prove that: sin3x=3sinx-4sin^3x

Prove that (sin3x + sinx)sinx + (cos3x - cosx)cosx = 0

Prove that cot4x(sin5x + sin3x) = 2cos4x cosx

ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. The number of integer x satisfying sin^(-1) |x -2| + cos^(-1) (1 -|3 -...

    Text Solution

    |

  2. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

    Text Solution

    |

  3. Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2

    Text Solution

    |

  4. If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1...

    Text Solution

    |

  5. Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...

    Text Solution

    |

  6. Let f(x)= cos^(-1) ((1-x^2)/(1+x^2))= 2 tan^(-1)x x ge 0 , =-2 tan^(-1...

    Text Solution

    |

  7. Let f(x)= sin^(-1)((2x)/(1+x^2))AAx in R. The function f(x) is continu...

    Text Solution

    |

  8. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

    Text Solution

    |

  9. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

    Text Solution

    |

  10. If tan^(-1) . b/(c+a) + tan^(-1) . (c)/(a + b) = pi/4where a, b, c , a...

    Text Solution

    |

  11. Solutions of sin^(-1) (sinx) = sinx are if x in (0, 2pi)

    Text Solution

    |

  12. The equation e^(sin^(-1)x)/pi=y/(log y) has

    Text Solution

    |

  13. Let f(x) =1+2sin(e^x/(e^x+1)) x ge 0 then f^(-1)(x) is equal to (assu...

    Text Solution

    |

  14. cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) is equal to

    Text Solution

    |

  15. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is

    Text Solution

    |

  16. If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...

    Text Solution

    |

  17. If tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2, then ...

    Text Solution

    |

  18. The number of solution of the equation |tan^(-1)|x||=sqrt((x^(2)+1)^(2...

    Text Solution

    |

  19. For any real number x ge 1, the expression sec^(2)x ( tan^(-1)x) - ...

    Text Solution

    |

  20. Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( x^(2) + x +...

    Text Solution

    |