Home
Class 11
MATHS
(sin5theta+sin2theta-sin tehta)/(cos5the...

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

A

`tan theta`

B

`cos theta`

C

`cot theta`

D

none of these

Text Solution

Verified by Experts

LHS `=(2sin2thetacos3theta+sin2theta)/(2cos3theta.cos2theta+2cos3theta+2cos^(2)theta) = (sin2theta[2cos3theta+1])/(2[cos3theta(cos2theta+1)+(cos^(2)theta)]`
`=(sin2theta[2cos3theta+1])/(2[cos3theta(2cos^(2)theta)+cos^(2)theta]) = (sin2theta[2costheta+1])/(2[cos3theta(cos2theta+1)+(cos^(2)theta)]`
`=(sin2theta[2cos3theta+1])/(2[cos3theta(2cos^(2)theta)+cos^(2)theta]) = (sin2theta(2cos3theta+1))/(2cos^(2)theta(2cos3theta+1))=tantheta` Ans.
Promotional Banner

Topper's Solved these Questions

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

    ALLEN|Exercise EXERCISE (S-1)|44 Videos

Similar Questions

Explore conceptually related problems

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

(sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos 7theta+cos9theta) is equal to

(sin5theta+sin3theta)/(cos5theta+cos3theta) is equal to

(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

sin theta+sin2 theta+sin3 theta=1+cos theta+cos2 theta

(sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7theta+cos9theta)=?

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] "then " f (pi/7) is

Prove that :(sin5 theta-2sin3 theta+sin theta)/(cos5 theta-cos theta)=tan theta

If cos theta =4/5 then sin^2 theta cos theta + cos^2 theta sin theta is equal to :

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 sin2A= lambda sin 2B prove that (tan(A+B)/tan(A-B))=(lambda+1)/(la...

    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)), B...

    Text Solution

    |

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

    Text Solution

    |

  17. In any triangle ABC, sinA -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: -4le5costheta+3cos(theta+pi/3)+3 ge10, for all values of t...

    Text Solution

    |

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

    Text Solution

    |