Home
Class 11
MATHS
In a right angled triangle, acute angle ...

In a right angled triangle, acute angle A and B satisfy `tanA+tanB+tan^2A+tan^2B+tan^3A+tan^3B=70.` Find the angle A and B in radians.

Text Solution

Verified by Experts

`A+B+90=180`
`A+B=90`
`B=90-A`
`tanB=tan(90-A)=cotA`
`tanB=1/(tanA)`
`(tanA+1/tanA)+(tan^2A+1/tan^2A)+(tan^3A+1/tan^3A)=70`
`(tanA+1/tanA)+(tanA+1/tanA)^2-2+(tanA+1/tanA)^3-3(tanA+1/tanA)=70`
Let`tanA+1/tanA=t`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

In a right triangle ABC, right angled at B, if tan A=1, then verify that 2sinAcosA=1.

In acute angled triangle ABC prove that tan ^(2)A+tan^(2)B+tan^(2)Cge9 .

In a triangle tan A+ tan B + tan C=6 and tan A tan B= 2, then the values of tan A, tan B and tan C are

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

The value of tan^2 A - tan^2 B is

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C

If two angles of a triangle are tan^(-1)(2)a n dtan^(-1)(3), then find the third angle.

In a right angle triangle ABC with right angle at B , in which a= 24 units , b = 25 units and angle BAC =theta , then find sin A tan A ( A lt 90 ^(@))

Find the angle A in triangle ABC, if angle B=60^∘ and angle c=70^∘

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

  2. The base B C of A B C is fixed and the vertex A moves, satisfying the...

    Text Solution

    |

  3. In a right angled triangle, acute angle A and B satisfy tanA+tanB+tan^...

    Text Solution

    |

  4. Solve sin^2x+cos^2y=2sec^2z for x , y ,a n dzdot

    Text Solution

    |

  5. If 0ltalphaltbetaltgammagtpi//2,then prove that tanalphalt(sinalpha+si...

    Text Solution

    |

  6. Given b=2,c=sqrt(3),/A=30^0 , then inradius of A B C is (sqrt(3)-1)/2...

    Text Solution

    |

  7. If A,B,C are angles of a triangle, then 2sin(A/2)cosec (B/2)sin(C/2)-s...

    Text Solution

    |

  8. Solve cos^(50)x-sin^(50)x=1

    Text Solution

    |

  9. Prove that: sqrt(1-sintheta)/sqrt(1+sintheta) = sec theta - tan thet...

    Text Solution

    |

  10. If two sides of a triangle are roots of the equation x^2-7x+8=0 and th...

    Text Solution

    |

  11. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

    Text Solution

    |

  12. If 3sinx+4cosa x=7 has at least one solution, then find the possible v...

    Text Solution

    |

  13. Prove that (cos(90^0+theta)sec(-theta)"tan"(180^0-theta))/(sec(360^0-t...

    Text Solution

    |

  14. Find the length of the tanget to a circle with centre 'O' and radius =...

    Text Solution

    |

  15. Prove that : sqrt((1+cos theta)/(1-costheta))=cosec theta+ cot theta.

    Text Solution

    |

  16. Find the number of solutions of sin^2x-sinx-1=0in[-2pi,2pi]

    Text Solution

    |

  17. Prove that sin(-420^0)(c0s390^0)+cos(-660^0)(sin330^0)=-1

    Text Solution

    |

  18. If R1 is the circumradius of the pedal triangle of a given triangle A ...

    Text Solution

    |

  19. If x=sin(theta+(7pi)/(12))+sin(theta-pi/(12))+sin(theta+(3pi)/(12))dot...

    Text Solution

    |

  20. In any triangle, the minimum value of r1r2r3//r^3 is equal to 1 (b) ...

    Text Solution

    |