Home
Class 12
MATHS
If tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-...

If `tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-C)/4=1` , then ` A B C` is equilateral (b) isosceles (c) scalene (d) none of these

A

equilateral

B

isosceles

C

scalene

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
Let `alpha=(pi-A)/(4),beta(pi-B)/(4),gamma=(pi-C)/(4)`
`rArr alpha+beta+gamma=(pi)/(2)`
`sum tan alpha tan beta=1`
`rArr sum tan^(2)alpha=1sum tan alpha tan beta`
`rArr tan alpha=tan beta=tan gamma`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If tan^2((pi-A)/4)+tan^2((pi-B)/4)+tan^2((pi-C)/4)=1 , then A B C is (A) equilateral (B) isosceles (C) scalene (D) none of these

In triangle ABC, if |[1,1,1], [cot (A/2), cot(B/2), cot(C/2)], [tan(B/2)+tan(C/2), tan(C/2)+ tan(A/2), tan(A/2)+ tan(B/2)]| then the triangle must be (A) Equilateral (B) Isoceless (C) Right Angle (D) none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

Prove that (1-tan^2(pi/4-A))/(1+tan^2(pi/4-A))=sin2Adot

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

If 3tan(theta-15^0)=tan(theta+15^0), then theta is equal to n in Z) n pi+pi/4 (b) npi+pi/8 npi+pi/3 (d) none of these

If (3-tan^2(pi/7))/(1-tan^2(pi/7))=kcos(pi/7) then the value of k is (a)1 (b) 2 (c) 3 (d) 4

If x in (pi,(3pi)/2), then 4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x) is always equal to (a) 1 (b) 2 (c) -2 (d) none of these

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If theta is eliminated from the equations x=a"cos"(theta-alpha) and y=...

    Text Solution

    |

  2. The minimum vertical distance between the graphs of y=2+s in xa n dy=c...

    Text Solution

    |

  3. If tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-C)/4=1 , then A B C is equila...

    Text Solution

    |

  4. If (1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)), then alpha is equ...

    Text Solution

    |

  5. If cos28^0+sin28^0=k^3, t h e ncos17^0 is equal to (k^3)/(sqrt(2)) (b...

    Text Solution

    |

  6. Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the va...

    Text Solution

    |

  7. If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y-1) is equal...

    Text Solution

    |

  8. If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2 , where x , y , in (0,pi/2), th...

    Text Solution

    |

  9. If cot^2x=cot(x-y)(x-z),t h e ncot2x is equal to (w h e r ex!=pi/4) ....

    Text Solution

    |

  10. In a A B C , if tanB :tanC=3:4:5, then the value of sinA sinB sinC is...

    Text Solution

    |

  11. find the value of sin 27^(@)-cos27^(@)?

    Text Solution

    |

  12. If costheta1 2costheta2, then tan(theta(1-theta2))/2tan(theta1+theta2)...

    Text Solution

    |

  13. Let alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+si...

    Text Solution

    |

  14. If n=pi/(4alpha), then tanalpha tan 2alpha tan 3 alpha........tan(2n-1...

    Text Solution

    |

  15. (sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7the...

    Text Solution

    |

  16. If x , y , z are in A.P., then (sinx-sinz)/(cosz-cosx) is equal to tan...

    Text Solution

    |

  17. If (cosx)/a=(cos(x+theta))/b=(cos(x+20))/c=(cos(x+3theta))/d then (a+c...

    Text Solution

    |

  18. If cos alpha + cos beta =0 = sin alpha + sin beta , then cos...

    Text Solution

    |

  19. Value of (3+cot80^0cot20^0)/(cot80^0+cot20^0) is equal to cot20^0 (b)...

    Text Solution

    |

  20. If tanalpha is equal to the integral solution of the inequality 4x^2-1...

    Text Solution

    |