Home
Class 11
MATHS
Solve the equation (sqrt(3))/2sinx-cosx=...

Solve the equation `(sqrt(3))/2sinx-cosx=cos^2x`

Text Solution

Verified by Experts

`sqrt3/2sinx=cos^2x+cosx`
`sqrt3sinx=2(cos^2x+cosx)`
`3sin^2x=4(cos^2x+cosx)^2`
`3(1-cos^2x)=4(cos^4x+2cos^3x+cos^2x)`
`4cos^4x+8cos^3x+7cos^2x-3=0`
`(cosx+1)(2cosx-1)(2cos^2x+3cosx+3)=0`
`cosx=-1,1/2`
`x=(2n+1)pi,2npi+pi/3`.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

Solve the equation sqrt(|sin^(-1)|"cosx"||+|cos^(-1)|sinx||)=sin^(-1)|cosx|-cos^(-1)|sinx|,(-pi)/2lt=xlt=pi/2dot

Solve the equation sqrt3cos x + sin x = sqrt2 .

Solve the equation: cos^2[pi/4(sinx+sqrt(2)cos^2x)]-tan^2[x+pi/4tan^2x]=1

Solve sqrt3 sin x+cos x=2

The number of solution of the equation |2sinx-sqrt(3)|^(2cos^2 x-3cosx+1)=1in[0,pi] is 2 (b) 3 (c) 4 (d) 5

Solve the equation 2(cos x+cos2x)+sin2x(1+2cos x)=2sinx for (-pilt=xlt=pi)

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx) is (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

Solve the equations: 2 cos^(2)x - 7 cos x + 3 = 0

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove that sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)=3/(16).

    Text Solution

    |

  2. Find the sign of the values of tan113^0-cos107^0=a and tan107^0-cos105...

    Text Solution

    |

  3. Solve the equation (sqrt(3))/2sinx-cosx=cos^2x

    Text Solution

    |

  4. If xsina+ysin2a+zsin3a=sin4a xsinb+ysin2b+zsin3b=sin4b, xsinc+ys...

    Text Solution

    |

  5. Prove that (sinx-cosx+1)/(sinx+cos-1)=secx+tanx.

    Text Solution

    |

  6. The lengths of the medians through acute angles of a right-angled t...

    Text Solution

    |

  7. If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x ...

    Text Solution

    |

  8. In triangle A B C ,tanA+tanB+tanC=6a n dtanAtanB=2, then the values o...

    Text Solution

    |

  9. If 2cosx+sinx=1, then find the value of 7cosx+6sinxdot

    Text Solution

    |

  10. If cos 25^0 + sin 25^0 = p, then cos 50^0 is equal to

    Text Solution

    |

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

    Text Solution

    |

  12. Find the values of xa n dy for which cosec theta=(x^2-y^2)/(x^2+y^2) i...

    Text Solution

    |

  13. The set of all x in the interval [0,pi] for which 2sin^2x-3sinx+1geq0 ...

    Text Solution

    |

  14. If in a triangle (1-(r1)/(r2))(1-(r1)/(r3))=2 then the triangle is rig...

    Text Solution

    |

  15. Find sum(n=1)^(oo)1/(n^2+5n+6)

    Text Solution

    |

  16. A parallelogram containing a 60^0 angle has perimeter p and its longer...

    Text Solution

    |

  17. If in a triangle (1-(r1)/(r2))(1-(r1)/(r3))=2 then the triangle is rig...

    Text Solution

    |

  18. If sin(sinx+cosx)=cos(cosx-sinx), and largest possible value of sinxi ...

    Text Solution

    |

  19. If 0lt=xlt=pi/3 then range of f(x)=sec(pi/6-x)+sec(pi/6+x) is (a)(4...

    Text Solution

    |

  20. The values of x1 between 0 and 2pi , satisfying the equation cos3x+c...

    Text Solution

    |