Home
Class 11
MATHS
4(sin^(6)theta+cos^(6)theta)-6(sin^(4)th...

`4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)`is equal to

A

0

B

1

C

`-2`

D

none of these

Text Solution

Verified by Experts

`4[(sin^(2)theta+cos^(2)theta)^(3) -3sin^(2)thetacos^(2)theta(sin^(2)theta+cos^(2)theta)]-6[(sin^(2)theta+cos^(2)theta)^(2)-2sin^(2)thetacos^(2)theta]`
`=4[1-3sin^(2)thetacos^(2)theta]-6[1-2sin^(2)thetacos^(2)theta]`
`=4-12sin^(2)thetacos^(2)theta-6+12sin^(2)thetacos^(2)theta=-2`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (JM)|8 Videos

Similar Questions

Explore conceptually related problems

2(sin^(6) theta + cos^(6)theta) - 3(sin^(4)theta + cos^(4)theta)+ 1 = 0

cos^(4)theta-sin^(4)theta is equal to

Which of the following values of a and b will make a(sin^(6)theta+cos^(6)theta)-b(sin^(4)theta+cos^(4)theta) independent of theta ?

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta) is equal to (a) 0 (b) 1 (c) -1 (d) None of these

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta) is equal to 0 (b) 1 (c) -1 (d) None of these

The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta is equal to

The value of Delta=|(1,sin 3theta, sin^(3)theta),(2cos theta, sin 6 theta, sin^(3)2 theta),(4cos^(2)theta-1,sin 9 theta, sin^(3)3theta)| equal to

Prove that sin^(4)theta-cos^(4)theta=sin^(2)theta-cos^(2)theta .

If sin^(6)theta+cos^(6) theta-1= lambda sin^(2) theta cos^(2) theta , find the value of lambda .

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
  1. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

    Text Solution

    |

  2. Show that log(4)18 is an irrational number.

    Text Solution

    |

  3. If in a right angled triangle, a and b are the lengths of sides and c ...

    Text Solution

    |

  4. If the arcs of same length in two circles subtend angles of 60^(@) and...

    Text Solution

    |

  5. If sintheta+sin^(2)theta=1, then prove that cos^(12)theta+3cos^(10)the...

    Text Solution

    |

  6. 4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)is equal to

    Text Solution

    |

  7. If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

    Text Solution

    |

  8. Prove that sqrt(3) " cosec "20^(@)-sec 20^(@)=4

    Text Solution

    |

  9. Prove that tan 70^(@)=cot70^(@)+2cot40^(@)

    Text Solution

    |

  10. If sin 2A=lambda sin 2B, prove that : (tan (A+B))/(tan(A-B)) = (lambda...

    Text Solution

    |

  11. (sin5theta+sin2theta-sin tehta)/(cos5theta+2cos3theta+2cos^(2)theta+co...

    Text Solution

    |

  12. Prove that: s in 12^0s in 48^0s in 54^0=1/8dot

    Text Solution

    |

  13. Prove that (2cos2A+1)/(2cos2A-1)=tan(60^0+A)tan(60^0-A)dot

    Text Solution

    |

  14. Prove that: tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A

    Text Solution

    |

  15. sin(671/2)^(@) + cos(671/2)^(@) is equal to A) 1/2sqrt(4+2sqrt(2)), ...

    Text Solution

    |

  16. The value of sin 78^@ - sin 66^@ - sin 42^@ + sin 6^@ is

    Text Solution

    |

  17. In a tringle ABC, sin A-cosB=cosC, then angle B, is

    Text Solution

    |

  18. If A+B+C =(3pi)/(2), then cos2A+cos2B+cos2C is equal to-

    Text Solution

    |

  19. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

    Text Solution

    |

  20. Find the maximum value of 1+sin(pi/4+theta) + 2cos(pi/4-theta).

    Text Solution

    |