Home
Class 11
MATHS
If (1+sint)(1+cost)=5/4 then find the v...

If `(1+sint)(1+cost)=5/4` then find the value of `(1-sint)(1-cost)dot`

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ (1 + \sin t)(1 + \cos t) = \frac{5}{4} \] ### Step 1: Expand the left-hand side We can expand the left-hand side: ...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

If (1+sint)(1+cost)=5/4dot Find the value (1-sint)(1-cos t)

If int_(0)^(1)(sint)/(1+t)dt=alpha , then find the value of int_(4pi-2)^(4pi)("sin"t/2)/(4pi|2-t|)dt

If x=(4/5)^(-2)-:(1/4)^2, find the value of x^(-1)dot

If ycost" and "x=sint, then what is the value of (dy)/(dx) ?

For the variable triangle ABC with fixed vertex C(1,2) and A,B having coordinates (cost, sint),( sint,-cost) respectively,find the locus of its centroid.

If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2) .

If int_(0)^(1)(sint)/(1+t)dt=alpha , them the value of the integral int_(4pi-2)^(4pi)("sin"(t)/(2))/(4pi+2-t)dt in terms of alpha is given by

If x=a(t+sint),y=a(1-cost)," then "(dy)/(dx)=

Find the equation of the tangent and the normal at the point 't' on the curve x=a(t+sint), y=a(1-cost)

If x = sint cos2t and y = cost sin2t , then at t = pi/4 , the value of dy/dx is equal to:

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. The value of f(x)=x^4+4x^3+2x^2-4x+7, when x=cot((11pi)/8) is

    Text Solution

    |

  2. Show that sqrt(3)cosec 20^@ - sec 20^@= 4

    Text Solution

    |

  3. If (1+sint)(1+cost)=5/4 then find the value of (1-sint)(1-cost)dot

    Text Solution

    |

  4. If alpha,beta,gamma,delta are the smallest positive angles in ascendi...

    Text Solution

    |

  5. (sin^2A-sin^2B)/(sinAcosA-sinBcosB)is equal to (a)"tan"(A-B) ...

    Text Solution

    |

  6. If cos25^0+sin25^0=p , then cos50^0 is (a)sqrt(2-p^2) (b) -sqrt(2...

    Text Solution

    |

  7. The value of cot((7pi)/16)+2cot((3pi)/8)+cot((15pi)/16) is (a)4 (b...

    Text Solution

    |

  8. If tan^2theta=2tan^2phi+1,t h e ncos2theta+sin^2phi equals (a)-1 (...

    Text Solution

    |

  9. If tanA.tanB=1/2,t h e n(5-3cos2A)(5-3cos2B)= (a)2 (b) 8 (c) 12 ...

    Text Solution

    |

  10. If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2...

    Text Solution

    |

  11. The value of cos^2 10^0-cos10^0cos50^0+cos^2 50^0 is equal to 4/3 (b)...

    Text Solution

    |

  12. If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the v...

    Text Solution

    |

  13. In A B C , if (sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c...

    Text Solution

    |

  14. If sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

    Text Solution

    |

  15. Prove that (cosA-cosB)^2+(sin A-sin B)^2=4sin^2((A-B)/2)

    Text Solution

    |

  16. Let f(x)=2 cosec 2x + sec x+cosec x, then the minimum value of f(x) fo...

    Text Solution

    |

  17. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

    Text Solution

    |

  18. Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tantheta))^2

    Text Solution

    |

  19. Prove that (1-tan^2(pi/4-A))/(1+tan^2(pi/4-A))=sin2Adot

    Text Solution

    |

  20. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

    Text Solution

    |