Home
Class 11
MATHS
If A+B=pi/4 , prove that: (1+t a n A)...

If `A+B=pi/4` , prove that: `(1+t a n A)(1+t a n B)=2` `(cotA-1)(cotB-1)=2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|166 Videos
  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|196 Videos

Similar Questions

Explore conceptually related problems

If A + B = (pi)/(4) , then prove that (1 + tan A) (1 + tan B) = 2

i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2

If A+B+C=pi , prove that: cotB cotC + cotC cotA + cotA cotB=1 .

If A-B=pi//4 , then (1+t a n A)(1-t a n B) is equal to 2 b. 1 c. 0 d. 3

If A+B+C=pi , prove that : (tanA+tanB+tanC) (cotA+cotB+cotC)=1+secA secB secC .

i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2 ii) If tan(picostheta)=cot(pisintheta) , then prove that: cos(theta-pi/4)=1/(2sqrt(2))

If A+B+C=pi , prove that : (cotA+cotB)/(tanA+tanB) + (cotB+cotC)/(tanB+tanC) + (cotC+cotA)/(tanC+tanA) =1

If A+B+C=pi , prove that : (cotB+cotC) (cotC+cotA) (cotA+cotB)=cosecA cosecB cosecC

If 3t a n At a n B=1, prove that 2cos(A+B)=cos(A-B)dot

Prove that: (sin(A-B))/(sinAsinB)' = cotB - cotA

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. If tan(A-B)=1,sec(A+B)=2/(sqrt(3)) , then the smallest positive value ...

    Text Solution

    |

  2. If t a nbeta=(nsinalphacosalpha)/(1-nsin^2alpha) , show that tan(alph...

    Text Solution

    |

  3. If A+B=pi/4 , prove that: (1+t a n A)(1+t a n B)=2 (cotA-1)(cot...

    Text Solution

    |

  4. Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-c...

    Text Solution

    |

  5. If tan(alpha+theta)=ntan(alpha-theta) , show that (n+1)sin2theta=(n-1...

    Text Solution

    |

  6. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

    Text Solution

    |

  7. If tan( pi cos theta) = cot ( pi sin theta) then sin (theta + pi/4) e...

    Text Solution

    |

  8. Find the values of the following: sin75^0 (ii) cos75^0 (iii) sin15^0...

    Text Solution

    |

  9. If cotalpha=1/2,secbeta=-5/3,where piltalphalt(3pi)/2and pi/2 ltbetalt...

    Text Solution

    |

  10. If sin A=3/5,0<A<pi/2a n dcosB=(-12)/(13),0<B<(3pi)/2, find the follow...

    Text Solution

    |

  11. Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(ta...

    Text Solution

    |

  12. Prove that: 1/(cos(x-a)cos(x-b))=(tan(x-b)-"tan"(x-a))/(sin(a-b))

    Text Solution

    |

  13. If sin(picostheta)=cos(pi sintheta),t h e n sin2theta=

    Text Solution

    |

  14. If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta...

    Text Solution

    |

  15. Prove that: 1/(sin(x-a)sin(x-b))=(cot(x-a)-"cot"(x-b))/(sin(a-b))

    Text Solution

    |

  16. If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi ...

    Text Solution

    |

  17. If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that si...

    Text Solution

    |

  18. Prove that: 1/(sin(x-a)cos(x-b))=(cot(x-a)+"tan"(x-b))/(cos(a-b))

    Text Solution

    |

  19. Find the maximum and minimum values of the following expressions. (i)...

    Text Solution

    |

  20. If sinA=3/5 and cosB=9/41, 0 < A < pi/2 and 0 < B < pi/2 then find the...

    Text Solution

    |