Home
Class 12
MATHS
If (x)/(cos theta)=(y)/(cos(theta-(2pi)/...

If `(x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(z)/(cos(theta+(2pi)/(3))), then x+y+z=`

A

1

B

0

C

`-1`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`(x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(1)/(cos(theta+(2pi)/(3)))`
Therefore each ratio is equal to
`(x+y+z)/(cos theta+cos(theta-(2pi)/(3)))=(x)/(cos(theta+(2pi)/(3)))=(x+y+z)/(0)`
or `x+y+z=0`
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 (x)/(cos theta)=(y)/(cos(theta-(2pi)/(2)))=(2)/(cos(theta+(2pi)/(3))), then x+y+z=

If (x)/(cos theta)=(y)/(cos(theta-(2 pi)/(3)))=(z)/(cos(theta+(2 pi)/(3))) then x+y+z is (a)1(b)0(c)-1(d) none of these

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), prove that xy+yz+zx=0

If x*cos theta=y*cos(theta+(2 pi)/(3))=2*cos(theta+(4 pi)/(3)) then evaluate xy+yz+zx

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), then write the value of (1)/(x)+(1)/(y)=(1)/(z)

If frac {x}{cos theta} = frac {y}{cos(theta -2pi/3)} = frac {z}{cos(theta +2pi/3)} then x + y + z is equal to

The value of the determinant |sin theta,cos theta,sin2 thetasin(theta+(2 pi)/(3)),cos(theta+(2 pi)/(3)),sin(2 theta+(4 pi)/(3))sin(theta-(2 pi)/(3)),cos(theta-(2 pi)/(3)),sin(2 theta-(4 pi)/(3))

If x=sin(theta+(7 pi)/(12))+sin(theta+(pi)/(12))+sin(theta+(3 pi)/(12))Y=cos(theta+(7 pi)/(12))+cos(theta+(pi)/(12))+cos(theta+(3 pi)/(12)) then prove that (X)/(Y)-(Y)/(X)=2tan2 theta

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If A,B,C are angles of a triangle, then 2sinA/2cos e c B/2sinC/2-sinAc...

    Text Solution

    |

  2. If a <= 3cosx+5sin(x-pi/6) <= b for all x, then (a,b) is

    Text Solution

    |

  3. If (x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(z)/(cos(theta+(2pi)/(3)...

    Text Solution

    |

  4. Let x=sin1^@ then find the value of the expression 1/(cos0^@cos1^@)+1/...

    Text Solution

    |

  5. If theta is eliminated from the equations x=a"cos"(theta-alpha) and y=...

    Text Solution

    |

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

    Text Solution

    |

  7. 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

    |

  8. if (1+tanalpha)(1+tan4alpha) =2 where alpha in (0 , pi/16) then alpha...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If y = (1 + tan A) (1 - tan B), where A -B=pi/4 then (y+ 1)^(y + 1) is...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB si...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Let alpha, beta be such that it pi < alpha - beta <3 pi. if sin alph...

    Text Solution

    |

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

    Text Solution

    |

  19. (sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos ...

    Text Solution

    |

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

    Text Solution

    |