Home
Class 12
MATHS
If tantheta+sintheta=mandtantheta-sinthe...

If `tantheta+sintheta=mandtantheta-sintheta=n`,then

A

`m^2-n^2=4mn`

B

`m^2+n^2=4mn`

C

`m^2-n^2=m^2+n^2`

D

`m^2-n^2=4sqrt(mn)`

Text Solution

Verified by Experts

The correct Answer is:
D
From the given relations,
`m+n=2tantheta,m-n=2sintheta`.
Thus,`m^2-n^2=4tanthetasintheta`
Also `sqrt(mn)=sqrt(tan^2theta-sin^2theta)=sinthetatantheta`
From Eqs. (i) and (ii), we get `m^2-n^2=4sqrt(mn)`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If a costheta+bsintheta=m and a sintheta-bcostheta=n," then Prove that " a^(2)+b^(2)=m^(2)+n,

If cos e ctheta-sintheta=ma n dsectheta-costheta=n ,"eliminate"theta

If tantheta+sectheta =x ,find sintheta

int_(sintheta)^(costheta)f(xtantheta)dx(w h e r etheta!=(npi)/2,n in I))i se q u a lto (a) -costhetaint_1^(tantheta)f(xsintheta)dx (b) -tanthetaint_(costheta)^(sintheta)f(x)dx (c) sinthetathetaint_1^(tantheta)f(xcostheta)dx (d) 1/(tantheta)thetaint_(sintheta)^(sinthetatantheta)f(x)dx

If tantheta=ntanalpha and sintheta=msinalpha then prove that cos^(2)theta=(m^(2)-1)/(n^(2)-1),n!=+-1.

If 5tantheta=4, then (5sintheta-3costheta)/(5sintheta+2costheta) is equal to 0 (b) 1 (c) 1/6 (d) 6

If sintheta,costheta and tantheta are in G.P., then prove that cot^(6)theta-cot^(2)theta=1

If tantheta+sectheta=1. 5 , find sintheta,tanthetaa n dsecthetadot

Prove that (tantheta +sectheta -1)/(tantheta-sectheta+1)=(1+sintheta)/costheta

CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. If tan theta = - (4)/(3), then sin theta is

    Text Solution

    |

  2. If sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to 2 (b) 2^n ...

    Text Solution

    |

  3. If tantheta+sintheta=mandtantheta-sintheta=n,then

    Text Solution

    |

  4. If cosectheta-cottheta=q, then the value of cosectheta is

    Text Solution

    |

  5. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

    Text Solution

    |

  6. If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta, then sin^2theta= 2...

    Text Solution

    |

  7. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

    Text Solution

    |

  8. If sec alphaa n dalpha are the roots of x^2-p x+q+0, then p^2=q(q-2) ...

    Text Solution

    |

  9. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

  10. If sinx+sin^2x=1, then find the value of cos^(12)x +3cos^(10)x + 3 cos...

    Text Solution

    |

  11. 3(sintheta-costheta)^4+6(sintheta +costheta)^2+4(sin^6theta+cos^6theta...

    Text Solution

    |

  12. If sinx+sin^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

    Text Solution

    |

  13. (1+tanalphatanbeta)^2+(tan"alpha"-tan"beta")^2= tan^2alphatan^2beta ...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. A circle is drawn in a sector of a larger circle of radius r , as show...

    Text Solution

    |

  16. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  17. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  18. Which of the following is correct?

    Text Solution

    |

  19. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  20. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |