Home
Class 12
MATHS
If sinx+sin^2x=1, then find the value of...

If `sinx+sin^2x=1`, then find the value of `cos^(12)x +3cos^(10)x + 3 cos^8x + cos^6x-1 `

Text Solution

Verified by Experts

The correct Answer is:
3
We have `sinx+sin^2x=1`
`or sinx=1-sin^2xorsinx=cos^2x`
Now, `cos^12x+3sin^10x+3sin^4x+sin^3x-2`
`=sin^6x+3sin^5x+3sin^4x-2`
`=(sin^2x)^3+3(sin^2x)^2sinx+3(sin^2x)`
`(sinx)^2+(sinx)^3-2`
`=(sin^2x+sinx)^3-2=(1)^3-2=-1`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

If cos (2 sin^(-1) x) = (1)/(9) , then find the value of x

Find the value of sin^(-1)x+sin^(-1)1/x+cos^(-1)x+cos^(-1)1/xdot

If cos x + cos^2 x=1 , then the value of sin ^4 x + sin ^6 x is equal to

cos ^(2) 2x -cos ^(2) 6x = sin 4x sin 8x

cos 6x = 32 cos ^(6) x - 48 cos ^(4) x + 18 cos ^(2) x-1

Find the value of x for which sin^(-1) (cos^(-1) x) lt 1 and cos^(-1) (cos^(-1) x) lt 1

Prove that sin^(6)x + cos^(6)x = 1 - 3 sin^(2) x cos^(2)x .

CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. If sec alphaa n dalpha are the roots of x^2-p x+q+0, then p^2=q(q-2) ...

    Text Solution

    |

  2. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

  3. If sinx+sin^2x=1, then find the value of cos^(12)x +3cos^(10)x + 3 cos...

    Text Solution

    |

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

    Text Solution

    |

  5. If sinx+sin^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

    Text Solution

    |

  6. (1+tanalphatanbeta)^2+(tan"alpha"-tan"beta")^2= tan^2alphatan^2beta ...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Which of the following is correct?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. The equation sec ^2 theta = ( 4xy )/( ( x+y)^2) is possible for x...

    Text Solution

    |

  15. If sintheta1+sintheta2+sintheta3, then costheta1+costheta2+costheta3 i...

    Text Solution

    |

  16. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  19. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)(2sin^2 180^0-1)...

    Text Solution

    |

  20. If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

    Text Solution

    |