Home
Class 11
MATHS
If tanA.tanB=1/2,t h e n(5-3cos2A)(5-3co...

If `tanA.tanB=1/2,t h e n(5-3cos2A)(5-3cos2B)=` (a)2 (b) 8 (c) 12 (d) 16

Text Solution

Verified by Experts

`tanA*tanB = 1/2`
`=>tanA = 1/(2tanB)`
`=>tan^2A = 1/(4tan^2B)`
Now, `(5-3cos2A)(5-3cos2B)`
`=(5-3((1-tan^2A)/(1+tan^2A)))(5-3((1-tan^2B)/(1+tan^2B)))`
`=((5+5tan^2A-3+3tan^2A)/(1+tan^2A))((5+5tan^2B-3+3tan^2B)/(1+tan^2B))`
`=((2+8tan^2A)/(1+tan^2A))((2+8tan^2B)/(1+tan^2B))`
`=4*((1+4tan^2A)/(1+tan^2A))((1+4tan^2B)/(1+tan^2B))`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2beta)= (a) 1/2 (b) (-1)/2 (c) 1/4 (d) (-1)/4

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

If x=t^2,y=t^3,t h e n(d^2y)/(dx^2)= (a) 3/2 (b) 3/((4t)) (c) 3/(2(t)) (d) (3t)/2

If cos(A-B)=3/5 and tan A tan B=2, then (a) cos A cos B=1/5 (b) sin A sin B=-2/5 (c) cos A cos B=-1/5 (d) sin A sin B=-1/5

If A+B+C=(3pi)/2, t h e ncos2A+cos2B+cos2C is equal to (a) 1-4cos Acos BcosC (b) 4sinAsinBsinC (c) 1+2cosAcosBcosC (d) 1-4sinAsinBsinC

sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is equal to (a)5 (b) 13 (c) 15 (d) 6

If sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A-B)= +-1 (b) +-1/2 (c) +-1/3 (d) +-1/4

The value of cos(1/2cos^(-1)(1/8)) is (a) 3/4 (b) -3/4 (c) 1/(16) (d) 1/4

If u=x^2+y^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) 20t^8 (c) 5/(16t^6) (d) non of these

If x_1=3 and x_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xrarroo)x_n is (a) -1 (b) 2 (c) sqrt(5) (d) 3

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. The value of cot((7pi)/16)+2cot((3pi)/8)+cot((15pi)/16) is (a)4 (b...

    Text Solution

    |

  2. If tan^2theta=2tan^2phi+1,t h e ncos2theta+sin^2phi equals (a)-1 (...

    Text Solution

    |

  3. If tanA.tanB=1/2,t h e n(5-3cos2A)(5-3cos2B)= (a)2 (b) 8 (c) 12 ...

    Text Solution

    |

  4. If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal t...

    Text Solution

    |

  5. The value of cos^2 10^0-cos10^0cos50^0+cos^2 50^0 is equal to 4/3 (b)...

    Text Solution

    |

  6. If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the v...

    Text Solution

    |

  7. In A B C , if (sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c...

    Text Solution

    |

  8. If sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

    Text Solution

    |

  9. Prove that (cosA-cosB)^2+(sin A-sin B)^2=4sin^2((A-B)/2)

    Text Solution

    |

  10. If tanalpha=1/7,sin beta=1/(sqrt(10)), prove thatalpha+2beta=pi/4

    Text Solution

    |

  11. Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tantheta))^2

    Text Solution

    |

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

    Text Solution

    |

  13. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

    Text Solution

    |

  14. Find the maximum and minimum values of cos^2theta-6sinthetacostheta+3s...

    Text Solution

    |

  15. If p(x)=sinx(sin^3x+3)+cosx(cos^3x+4)+(1/2)sin^2 2x+5, then find the ...

    Text Solution

    |

  16. The value of cos e cpi/(18)-4sin(7pi)/(18) is

    Text Solution

    |

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

    Text Solution

    |

  18. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

    Text Solution

    |

  19. If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is eq...

    Text Solution

    |

  20. Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

    Text Solution

    |