Home
Class 12
MATHS
If (secA+tanA)(secB+tanB)(secC+tanC)=(se...

If `(secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC)`, prove that value of each side is `pm1`.

Text Solution

Verified by Experts

Let
`(secA+tanA)(secB+tanB)(secC+tanC)=x (i)`
`:. (secA-tanA)(secB-tanB)(secC-tanC)=x (ii)`
Multiplying Eqs.(i) and (ii), we get
`(sec^2A-tan^2A)(sec^2B-tan^2B)(sex^2C-tan^2C)=x^2`
or `x^2=1`
`:. x=pm1`
Hence, each side is equal to `pm1`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise example|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercises 2.1|8 Videos

  • TRIGONOMETRIC EQUATIONS

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

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If (secA+tanA)(secB+tanB)(secC+tanC)= (secA-tanA)(secB-tanB)(secC-tanC), prove that the value of each side is +-1.

if (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB) (secC-tanC) Prove that each of the side is equal to +-1.

Prove: (secA+tanA-1)(secA-tanA+1)=2tanA

Prove that : (secA-tanA)/(secA+tanA)=1-2secAtanA+2tan^(2)A

Prove that : (secA+1)/(tanA)=(tanA)/(secA-1)

prove that (1)/(secA - tanA) = secA + tanA

Prove that (cotA+tanB)/(cotB+tanA)=cotAtanB

Prove that (tanA)/(1+secA) - (tanA)/(1-secA) = 2cosecA

Prove: (secA-tanA)/(secA+tanA)=(cos^2A)/((1+sinA)^2)

Prove that 1/(secA-tanA)-1/(cosA)=1/cosA-1/(secA-tanA) .

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. If (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC)...

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. The value of (tan^(2)20^(@)-sin^(2)20^(@))/(tan^(2)20^(@).sin^(2)20^(@...

    Text Solution

    |

  6. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

    Text Solution

    |

  7. In DeltaABC, if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cos...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

    Text Solution

    |

  12. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

    Text Solution

    |

  13. If x,y,z be all positive acute angles then the least value of tanx(cot...

    Text Solution

    |

  14. Three circles each of radius 1, touch one another externally and they ...

    Text Solution

    |

  15. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |