Home
Class 12
MATHS
Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx...

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

Text Solution

AI Generated Solution

To evaluate the expression \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) at \( x = \frac{1}{5} \), we can follow these steps: ### Step 1: Use the identity for inverse trigonometric functions We know that: \[ \sin^{-1} x + \cos^{-1} x = \frac{\pi}{2} \] Thus, we can rewrite the expression: ...
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

Find the value of cos(2cos^(-1)x+sin^(-1)x) at x=(1)/(5), where 0<=pi and -(pi)/(2)<=sin^(-1)x<=(pi)/(2)

Find the value of cos( 2 cos^(-1) x + sin^(-1) x) " when " x = 1/5

If x=(1)/(5) , the value of cos(cos^(-1)x+2sin^(-1)x) is :

Find the value of cos[cos^-1 x+sin^-1 x] at x =1/5

Find the value of sin ( 2 cos^(-1) x + sin^(-1) x) " when " x = 1/5

If x in [1, 0) , then find the value of cos^(-1) (2x^(2) - 1) - 2 sin^(-1) x

If x in [-1, 0) then find the value of cos^(-1) (2x^(2) -1) -2 sin^(-1) x

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find the value of xdot

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Prove that: sin^(-1)((63)/(65))=sin^(-1)(5/(13))+cos^(-1)(3/5)

    Text Solution

    |

  16. Solve the following equation for x : 3sin^(-1)(2x)/(1+x^2)-4cos^(-1)(...

    Text Solution

    |

  17. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

    Text Solution

    |

  18. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

    Text Solution

    |

  19. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

    Text Solution

    |

  20. Find the principal values of (a) sin^(-1)((sqrt(3))/2) (b) sin^(-1)(...

    Text Solution

    |