Home
Class 12
MATHS
If ("cos"(x-y))/("cos"(+y))+("cos"(z+t))...

If `("cos"(x-y))/("cos"(+y))+("cos"(z+t))/(cos(z-t))=0` , then the value of expression `tanxtanytanztant` is equal to 1 (b) `-1` (c) 2 (d) `-2`

A

1

B

`-1`

C

2

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
`(cos(x-y))/(cos(x+y))+(cos(z+t))/(cos(z-t))=0`
or `(1+tan x tan y)/(1-tan x tan y)+(1-tan z tan t)/(1+tan z tan t)=0`
or `1+tan z tan t+tan x tan y+tan x tan y tan z tan t`
or `tan x tan y tan z tan t =-1`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Exercise (Multiple Correct Answer Type)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Exercise (Linked Comprehension Type)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Concept App. 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

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

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If ("cos"(x-y))/("cos"(x+y))+("cos"(z+t))/(cos(z-t))=0 , then the value of expression tanxtanytanztant is equal to (a) 1 (b) -1 (c) 2 (d) -2

If y=sqrt((1-cos2x)/(1+cos2x)) ,then the value of dy/dx will be

If cos (x-y)+1=0, then the value of (cos x+ cos y) and (sin x+sin y) is-

If cos x + cos y = 2, "then the value of" sin(x + y) is-

If y = sqrt((1-cos 2x)/(1+cos 2x)) , then the value of (dy)/(dx) will be

If (cos^2 x + 1/(cos^2 x)) (1 + tan^2 2y)(3 + sin 3z) = 4 ,then

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x=2 cos t+cos 2t and y=2 sin t-sin2t , then the value of (dy)/(dx) at t=(pi)/(4) is -

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)(1/x)+cos^(-1)(1/y)

If cos (x-y) =-1, then the values of (cos x+ cos y) and (sin x + sin y) are respectively-

CENGAGE PUBLICATION-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to 4x ...

    Text Solution

    |

  2. If cos2B=(cos(A+C))/("cos"(A-C)), then tanA ,t a n B ,tanC are in A.P....

    Text Solution

    |

  3. If ("cos"(x-y))/("cos"(+y))+("cos"(z+t))/(cos(z-t))=0 , then the value...

    Text Solution

    |

  4. If tan beta=2sin alpha sin gamma co sec(alpha+gamma), then cot alpha,c...

    Text Solution

    |

  5. The value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

    Text Solution

    |

  6. If cos^3xsin2x=sum(r=0)^n axsin(r x),AAx in R then

    Text Solution

    |

  7. tan^6pi/9-33tan^4pi/9+27tan^2pi/9 is equal to (a) 0 (b) sqrt(3) (c)...

    Text Solution

    |

  8. Given that a , b , c , are the side of a A B C which is right angled ...

    Text Solution

    |

  9. If theta=3alpha and sin theta=(a)/(sqrt(a^(2)+b^(2)) , the value of th...

    Text Solution

    |

  10. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

    Text Solution

    |

  11. In triangle A B C , if angle is 90^0 and the area of triangle is 30 sq...

    Text Solution

    |

  12. If sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A...

    Text Solution

    |

  13. In a right angled triangle the hypotenuse is 2sqrt(2) times the perpen...

    Text Solution

    |

  14. A circular ring of radius 3 cm hangs horizontally from a point 4 cm ve...

    Text Solution

    |

  15. The distance between two parallel lines is unity. A point P lies betwe...

    Text Solution

    |

  16. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

    Text Solution

    |

  17. If A+B+C=(3pi)/2, t h e ncos2A+cos2B+cos2C is equal to 1-4cos Acos Bc...

    Text Solution

    |

  18. If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta), then

    Text Solution

    |

  19. In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to 2sinAsi...

    Text Solution

    |

  20. The value of sum(r=0)^(10)cos^3(rpi)/3 is equal to 1/4 (b) 1/8 (c) -...

    Text Solution

    |