Home
Class 12
MATHS
The number of real solutions of the equa...

The number of real solutions of the equation `sqrt(1+cos2x)=sqrt(2)sin^(-1)(sinx),-pilt=xlt=pi` is (a) 0 (b) 1 (c) 2 (d) infinite

Text Solution

Verified by Experts

`cos2x=2cos^2x-1`
`sqrt(1+2cos^2x-1)=sqrt2 (sin^1sinx)/x`
`sqrt2 |cosx|=sqrt2 sin^-1sinx`
`2 solution`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

  • LINEAR PROGRAMING

    RD SHARMA ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^(-1)(sinx),-pilt=xlt=pi is 0 (b) 1 (c) 2 (d) infinite

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

The number of real solutions of the equation sqrt(1+cos2x) = sqrt(2)cos^(-1)(cosx) in [pi/2,pi] is

The number of real solution(s) of the equation sin^(-1)sqrt(x^(2)-x+1)+cos^(-1)sqrt(x^(2)-x)=pi is/are

Find the number of real solutions of the equation sin^(-1)(e^(x))+cos^(-1)(x^(2))=pi//2 .

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

The number of solutions for the equation sin^(-1) sqrt((x^(2)-x+1))+cos^(-1)sqrt((x^(2)-x))=pi is :

The number of real solutions of the equation -x^2+x-1=sin^4x is (A) 1 (B) 2 (C) 0 (D) 4

The number of solutions of the equation sin^3xcosx+sin^2xcos^2x+sinxcos^3x=1 in the interval [0,2pi] is/are 0 (b) 2 (c) 3 (d) infinite

RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The domain of cos^(-1)(x^2-4) is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}] .

    Text Solution

    |

  20. Find the domain of the function f(x)=sin^(-1)(2x-3) .

    Text Solution

    |