Home
Class 12
MATHS
Prove that, (1+tanA)^2 + (1-tanA)^2 = 2...

Prove that, `(1+tanA)^2 + (1-tanA)^2 = 2sec^2A`

Text Solution

Verified by Experts

The motion of the particle on the circles is shown with bold lines in the figure starting at `A_(0)(1,0)`. Note that on every circle the particle tracels just 1 rad. The particle crosses the positive direction of the x-axis first time on `C_(n)`, where n is the least positive integer such that `nge2pirArrn=7`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise example|10 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.1|8 Videos
  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos
  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

Prove that, ( 1-tan^2A) / (cot^2A-1) = tan^2A

Prove that, log_(2)2=1

Prove that (2tan^2 (30^@))/(1-tan^2(30^@))+sec^2(45^@)-cot^2(45^@) = sec(60^@) .

prove that , sec ^(2) ( tan ^(-1 )2) + "cosec"^(2) ( cot ^(-1) 3) = 15 .

Prove that : (tan theta+cot theta)^2=sec^2 theta+cosec^2 theta=sec^2 theta cosec^2 theta

If A+B=90^(@) then prove that 1+(tanA)/(tanB)=sec^(2)A.

Prove that : (2tan^(2)30^(@))/(1-tan^(2)30^(@))+sec^(2)45^(@)-cot^(2)45^(@)=sec60^(@) .

Prove that if tanA=1/7 and tanB=1/3 then cos2A=sin4B

Prove that, (cot theta - tan theta)/(1-2 sin ^(2) theta) = sec theta "cosec" theta

Prove that , (1+sec 2 theta) (1+sec2^(2) theta)(1+ sec2^(3)theta)... ( 1+sec 2^(2) theta) = (tan 2^(n) theta)/tan theta

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Prove that, (1+tanA)^2 + (1-tanA)^2 = 2sec^2A

    Text Solution

    |

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

    Text Solution

    |

  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

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

    Text Solution

    |

  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    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. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    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. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

    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

    |