Home
Class 12
MATHS
3(sintheta-costheta)^4+6(sintheta+costhe...

`3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)` is equal to 11 (b) 12 (c) 13 (d) 14

A

11

B

12

C

13

D

10

Text Solution

Verified by Experts

The correct Answer is:
C
`3(sintheta-costheta)^4+6(sintheta-costheta)^2+4(sin^6theta+cos^6theta)`
`=3[sin^4theta+cos^4theta-4sin^3thetacostheta`
`+6sin^2cos^2theta-4sinthetacos^3theta]+6[1+2sinthetacostheta]`
`+4[sin^4theta+cos^4theta-sin^2thetacos^2theta]`
`=7[sin^4theta+cos^4theta]+14sin^2thetacos^2theta-12 sinthetacostheta+6+12sinthetacostheta`
`=7(sin^2theta+cos^2theta)^2+6=13`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

(costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

If 5tantheta=4, then (5sintheta-3costheta)/(5sintheta+2costheta) is equal to

If tantheta =3," then " (sintheta-costheta)/(sintheta+costheta) is equal to

int(cos2theta)/((sintheta+costheta)^2)d theta is equal to

(sin5theta+sin2theta-sintheta)/(cos5theta+2cos3theta+2cos^2theta+costheta) is equal to

If 3sintheta+4costheta=5 ,then 4sintheta-3costheta=

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

4costheta cos 2theta cos3theta - 2cos 4theta=1

If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta) is equal to

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

  2. If sinx+sin^2x=1n then the value of cos^12x+3cos^10x+3cos^8x+cos^6x-1 ...

    Text Solution

    |

  3. 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)...

    Text Solution

    |

  4. If secx+sec^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

    Text Solution

    |

  5. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

    Text Solution

    |

  6. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  7. A circle is drawn in a sector of a larger circle of radius r , as show...

    Text Solution

    |

  8. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  9. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  10. Which of the following is correct?

    Text Solution

    |

  11. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  12. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

  13. sec^2theta=4xy/(x+y)^2 is true if and only if

    Text Solution

    |

  14. If sinx+siny+sinz=3," then "cosx+cosy+cosz is equal to

    Text Solution

    |

  15. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+si...

    Text Solution

    |

  16. Prove that, SinA/(1-cosA) =CosecA+cotA

    Text Solution

    |

  17. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  18. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 18...

    Text Solution

    |

  19. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right an...

    Text Solution

    |

  20. If sintheta+costheta=1/5and 0lethetaltpi" then "cottheta is

    Text Solution

    |