Home
Class 11
MATHS
Prove each of the following identities :...

Prove each of the following identities :
` (i) sin^(6) theta + cos^(6)theta = 1- 3 sin^(2) theta cos^(2) theta `
`(ii) sin^(2)theta + cos^(4) theta = cos^(2) theta + sin^(4) theta `
`(iii) "cosec"^(4) theta - "cosec"^(2) theta = cot^(4) theta + cot^(2) theta `

A

0

B

`-1`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|39 Videos

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    TARGET PUBLICATION|Exercise EVALUATION TEST|12 Videos

Similar Questions

Explore conceptually related problems

Prove each of the following identities : (1+ cos theta - sin^(2) theta)/(sin theta (1+ cos theta)) = cot theta

Prove that : sin^(4)theta + cos^(4)theta = 1 - 2 cos^(2) theta + 2 cos^(4)theta

Show that none of the following is an identity: (i) cos^(2) theta + cos theta =1 " " (ii) sin^(2) theta + sin theta =2 " " (iii) tan^(2) theta + sin theta = cos^(2) theta

Prove that : (sin^(4)theta- cos^(4) theta+ 1) "cosec"^(2)theta=2

Prove each of the following identities : (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta

Prove that (sin^(4)theta-cos^(4)theta)/(sin^(2)theta-cos^(2)theta)=1

TARGET PUBLICATION-TRIGONOMETRIC FUNCTIONS -COMPETITIVE THINKING
  1. If cosec theta - cot theta = 1/2, 0 lt theta lt pi/2, then cos theta...

    Text Solution

    |

  2. If cosec A + cot A =11/2 , then tan A equal to

    Text Solution

    |

  3. If sec theta + tan theta =p, then tan theta is equal to

    Text Solution

    |

  4. If t a ntheta+s e ctheta, then costheta equals (e^x+e^(-x))/2 (b) 2/(...

    Text Solution

    |

  5. If sin theta + cos theta =1 then sin theta cos theta =

    Text Solution

    |

  6. If 3 sin A+5 cos A =5, then the value of (3 cos A-5 sin A )^(2) is

    Text Solution

    |

  7. If sectheta=m, tantheta = n, then 1/m{(m+n)+1/(m+n)}

    Text Solution

    |

  8. If sintheta +cos theta =m and sec theta + cosec theta =n then n(m+1)(m...

    Text Solution

    |

  9. If 2y cos theta =x sin theta and 2x sec theta -y cosec theta =3, then ...

    Text Solution

    |

  10. If tan theta + sin theta = 1, " then" cos^(2) theta = n " then" m^(2)...

    Text Solution

    |

  11. If (secalpha+tanalpha)(secbeta+tanbeta)(secgamma+tangamma)=tanalphatan...

    Text Solution

    |

  12. If Pn = cos^n theta+ sin^n theta then 2P6-3P4 + 1 =

    Text Solution

    |

  13. Prove: (secA+tanA-1)(secA-tanA+1)=2tanA

    Text Solution

    |

  14. 17.cos^4theta- sin^4theta is equal to (a) 1 -2 sin^2(theta/2) (b)2c...

    Text Solution

    |

  15. Prove each of the following identities : (i) sin^(6) theta + cos^(6...

    Text Solution

    |

  16. Find the value of 6(sin^6theta+cos^6theta)-9(sin^4theta+cos^4theta)+...

    Text Solution

    |

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

    Text Solution

    |

  18. The value of k, for which (cos x+ sin x)^(2) +k sin x cos x-1 =0 is...

    Text Solution

    |

  19. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if x+y!=0 (b) x=...

    Text Solution

    |

  20. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)^(...

    Text Solution

    |