Home
Class 12
MATHS
If cos(A-B)=3/5 and tanAtanB=2 then...

If `cos(A-B)=3/5` and `tanAtanB=2` then

A

`cosA cos B = 1/5`

B

`sin A sin B=-2/5`

C

`cosA cos B=-1/5`

D

`sin A sin B= 1//5`

Text Solution

Verified by Experts

The correct Answer is:
A
(1) `cot(A-B)=(3)/(5)`
or `5cosA cosB+5sin A sin B=3`
From the second relation, we have
`sin A sin B=2cos A cos B`
`rArr cosA cos B=(1)/(5)` and `sin A sin B=(2)/(5)`
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 cos(A-B) = 3/5 and tanA.tanB=2, then

If cos(A-B)=3/5and tan A tanB=2, then

If cos(A-B)=(3)/(5) andtan Atan B=2, then cos A cos B=(1)/(5)(b)sin A sin B=-(2)/(5)cos A cos B=-(1)/(5)(d)sin A sin B=-(1)/(5)

If cos(A-B)=(3)/(5) and tan A tan B=2 then

If cos(A-B)=(3)/(5) and tan A tan B=2 then

If cos(A-B)=(3)/(5) and tan A tan B=2 then

If cos(A-B)=(3)/(5) and tan A tan B=2,thencos A cos B=(1)/(5) b.cot cos B=-(1)/(5)cs in As in B=-(1)/(5)ds in As in B=-(1)/(5)

If cos(A-B)=3//5andtanA.tanB=2, evalute : cosA.cosB.

If cos(A-B)=(3)/(5) and tan A tan B = 2, then

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If cos(A-B)=3/5 and tanAtanB=2 then

    Text Solution

    |

  2. If A=sin45^0+cos45^0a n dB=sin44^0, then A>B (b) A<B (c) A=B (d) none ...

    Text Solution

    |

  3. tan100^0+tan125^0+tan100^0tan125^0 is equal to

    Text Solution

    |

  4. If cos(alpha+beta)=0 then sin(alpha+2beta)=

    Text Solution

    |

  5. In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2...

    Text Solution

    |

  6. Let (sin(theta-alpha))/("sin"(theta-beta))=a/b a n d(cos(theta-alpha))...

    Text Solution

    |

  7. If A,B,C are angles of a triangle, then 2sinA/2cos e c B/2sinC/2-sinAc...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |