Home
Class 11
MATHS
Prove that cos ((3pi)/(4)+x)-cos ((3pi)/...

Prove that `cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x`

Text Solution

Verified by Experts

The correct Answer is:
`-sqrt2 sin x`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • TRIGONOMETRY

    FULL MARKS|Exercise Exercise 3.1|12 Videos

  • SOLVED PAPER 10

    FULL MARKS|Exercise PART-IV|8 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    FULL MARKS|Exercise Additional Questions Solved|19 Videos

Similar Questions

Explore conceptually related problems

Prove that cos ((pi)/(4) + x) + cos ((pi)/(4) -x) = sqrt2 cos x

Prove that cos (pi/4-x) cos (pi/4-y)- sin (pi/4-x) sin(pi/4-y) =sin (x+y)

Prove that 32 (sqrt(3)) sin"" (pi)/(48) cos"" (pi)/(48) cos"" (pi)/(24) cos"" (pi)/(12) cos"" (pi)/(6) = 3

Prove that cos^(2)x + cos^(2)(x + (pi)/(3)) + cos^(2) (x - (pi)/(3)) = (3)/(2)

Prove that int_(0)^(pi/4)(sin2xdx)/(sin^(4)x+cos^4 x)=(pi)/(4)

Find cos (x - y), given that cos x = - (4)/(5) with pi lt x lt (3pi)/(2) and sin y = - (24)/(25) with pi lt y lt (3pi)/(2) .

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

cos ((3pi )/( 2 ) + x) cos (2pi + x) [cot ((3pi)/( 2)- x ) + cot (2pi +x) ]=1

Prove that pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)

FULL MARKS-TRIGONOMETRY-Exercise 3.12
  1. Prove that cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x

    Text Solution

    |

  2. (1)/(cos 80^(@)) - (sqrt(3))/(sin 80^(@)) =

    Text Solution

    |

  3. If cos 28^(@) + sin 28^(@) = k^(3), then cos 17^(@) is equal to

    Text Solution

    |

  4. The maximum value of 4 sin^(2) x + 3 cos^(2) x + sin ""(x)/(2) + cos""...

    Text Solution

    |

  5. (1 + cos"" (pi)/(8))(1 + cos"" (3pi)/(8)) (1 + cos"" (5pi)/(8))(1 + co...

    Text Solution

    |

  6. If pi lt 2 theta lt (3pi)/(2), then sqrt(2 + sqrt( 2 + 2 cos 4 theta))...

    Text Solution

    |

  7. If tan 40^(@) = lambda, then (tan 140^(@) - tan 130^(@))/(1 + tan 140^...

    Text Solution

    |

  8. cos 1^(@) + cos 2^(@) + cos 3^(@) + ….+ cos 179^(@) =

    Text Solution

    |

  9. Letf(4)(x) = (1)/(k) [ sin^(k) + cos^(k) x ] where x in RR and k ge1. ...

    Text Solution

    |

  10. Which of the following is not true?

    Text Solution

    |

  11. cos 2theta cos 2phi + sin^(2) (theta - phi ) - sin^(2) ( theta + phi) ...

    Text Solution

    |

  12. (sin(A - B))/(cos A cos B) + (sin (B - C))/( cos B cos C) + (sin(C - A...

    Text Solution

    |

  13. If cos ptheta + cos qtheta = 0 and if p ne q, then theta is equal to (...

    Text Solution

    |

  14. If tan alpha and tan beta are the roots of x^(2) + ax + b = 0, then (s...

    Text Solution

    |

  15. In a triangle ABC, sin^(2)A + sin^(2)B + sin^(2)C = 2, then the triang...

    Text Solution

    |

  16. If f(theta) = |sin theta| + |cos theta|,theta in RR, then f(theta) is ...

    Text Solution

    |

  17. (cos 6x + 6 cos 4x + 15 cos 2x + 10)/(cos 5x + 5 cos 3x + 10 cos x ) i...

    Text Solution

    |

  18. The triangle of maximum area with constant perimeter 12m

    Text Solution

    |

  19. A wheel is spinning at 2 radians/second. How many seconds will it take...

    Text Solution

    |

  20. If sin alpha + cos alpha = b, then sin 2alpha is equal to

    Text Solution

    |

  21. In a DeltaABC, if (i)sin (A)/(2) sin"" (B)/(2) sin"" (C )/(2) gt 0 (...

    Text Solution

    |