Home
Class 12
MATHS
Evaluate: sin{cos^(-1)(-(3)/5)+cot^(-1)(...

Evaluate: `sin{cos^(-1)(-(3)/5)+cot^(-1)(-5/(12))}`

Text Solution

Verified by Experts

Let,`cos^(-1)(-(3)/5)=x`
`cot^(-1)(-5/(12))`=y
Then,`cosx=-3/5`
`coty=-5/12`
When,`cosx=-3/5` then `sinx=4/5`
by formula `1+cot^2y=cosec^2y`
when `coty=-5/12` then `cosecy=13/12` or `siny=12/13` or `cosy=-5/13`
...
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos
  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

solve sin{cos^(-1)(-(3)/(5))+cot^(-1)(-(5)/(12))}

Evaluate sin[2cos^(-1)(-3/5)] .

Evaluate: sin(cos^(-1)(3)/(5)+csc^(-1)(13)/(5))

Evaluate: sin{cos^(-1)(-(3)/(5))}( ii) tan{cos^(-1)(-(12)/(13))}

Evaluate (i) sin (cos^(-1) (3/5))

Evaluate: i) sin(cos^(-1)(3/5)) , ii) cos(tan^(-1)(3/4))

Evaluate cos(sin^(-1)(4/5)+cos^(-1)(2/3))

Find the value of tan(sin^(-1)((3)/(5))+cot^(-1)((3)/(2)))

Evaluate: cos{sin^(-1)(-(7)/(25))}( ii) sec{cot^(-1)(-(5)/(12))}cot{sec^(-1)(-(13)/(5))}

Find the value of tan (cos^(-1) (4/5)+ cot^(-1)(3/2)) .

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

    Text Solution

    |

  2. Evaluate: (i) tan{cos^(-1)(-7/(25))} (ii) "c o s e c"{cot^(-1)(-(12)/...

    Text Solution

    |

  3. Evaluate: sin{cos^(-1)(-(3)/5)+cot^(-1)(-5/(12))}

    Text Solution

    |

  4. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=(2pi)/3, find the valu...

    Text Solution

    |

  5. If tan^(-1)x+tan^(-1)y=(4pi)/5, find cot^(-1)x+cot^(-1)ydot

    Text Solution

    |

  6. If tan^(-1)x-cot^(-1)x=tan^(-1)""1/(sqrt(3)) find the value of xdot

    Text Solution

    |

  7. If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find the value of xdot

    Text Solution

    |

  8. If cos(sin^(-1)(2/5)+cos^(-1)x)=0 find the value of xdot

    Text Solution

    |

  9. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

    Text Solution

    |

  10. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

    Text Solution

    |

  11. If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/...

    Text Solution

    |

  12. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

    Text Solution

    |

  13. If alpha=tan^(-1)(t a n(5pi)/4)a n dbeta=tan^(-1)(-tan(2pi)/3),t h e n...

    Text Solution

    |

  14. The domain of cos^(-1)(x^2-4) is (a) [3,5] (b) [-1,1] (c)[-sqrt(5),-...

    Text Solution

    |

  15. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1...

    Text Solution

    |

  16. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

    Text Solution

    |

  17. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

    Text Solution

    |

  18. Solve the equation of x:sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

    Text Solution

    |

  19. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

    Text Solution

    |

  20. Prove that : tan^(-1)((63)/(16))=sin^(-1)((5)/(13))+cos^(-1)((3)/(5))

    Text Solution

    |