Home
Class 10
MATHS
Verify that: (i) cos60^@=cos^2 30^@-si...

Verify that: (i) `cos60^@=cos^2 30^@-sin^2 30^@=1/2` (ii) `4(sin^4 30^@+cos^4 60^@)-3(cos^2 45^@-sin^2 90^@)=2`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

What is the value of 4(sin^4 30^@ + cos^4 60^@) -3(cos^2 45^@ - sin^2 90^@) ?

cos^(2)30^@-sin^(2)30^@=cos60^@

Evaluate : (5 cos^(2)60^@+4cos^(2)30^@ - tan^(2)45^@)/(sin^(2) 30^@+cos^2 60^@)

Verify that : sin60^(@)=2sin30^(@)cos30^(@)

Find the value of 4(sin^(4)30^(@)+cos^(4)30^(@))-3(cos^(2)45^(@)+sin^(2)90^(@)) .

(cos 60^(@) xx cos 30^(@)+sin 60^(@)xx sin 30^(@))/(2 sin 30^(@) xx cos 0^(@)+ sin 90^(@))=?

sin^(2)30+cos^(2)60

Evaluate: (sin^(4) 60^(@) + sec^(4) 30^(@)) - 2 (cos^(2) 45^(@) - sin^(2) 90^(@))

Show that (i) cos60^(@)*cos30^(@)-sin60^(@)*sin30^(@)=cos90^(@) (ii) cos60^(@)=1-2sin^(2)30^(@)=2cos^(2)30^(@)-1 (iii) (tan60^(@)-tan30^(@))/(1+tan60^(@)*tan30^(@))=tan30^(@)

Evaluate: (sin^(4) 60^(@) + sec^(4)30^(@)) - 2(cos^(2)45^(@) - sin^(2) 90^(@))

RD SHARMA-TRIGONOMETRIC RATIOS-All Questions
  1. If x=30^@ , verify that : (i) tan2x=(2tanx)/(1-tan^2x) (ii) sinx=sqr...

    Text Solution

    |

  2. Verify that: sin60o=(2tan30o)/(1+tan^2 30o)=(sqrt(3))/2 (ii) cos60...

    Text Solution

    |

  3. Verify that: (i) cos60^@=cos^2 30^@-sin^2 30^@=1/2 (ii) 4(sin^4 30^...

    Text Solution

    |

  4. If theta is an acute angle and sintheta=costheta , find the valu...

    Text Solution

    |

  5. Given that sin(A+B)=sinAcosB+cosAsinB , find the value of sin75^@ .

    Text Solution

    |

  6. In a rectangle A B C D ,\ \ A B=20 c m , /B A C=60o . Calculate ...

    Text Solution

    |

  7. Evaluate the following: (i) sin45osin30o+cos45ocos30o (ii) sin60oc...

    Text Solution

    |

  8. Evaluate the following: (i) cos60ocos45o-sin60osin45o (ii) sin^2 3...

    Text Solution

    |

  9. Evaluate the following: cos^2 30o+cos^2 45o+cos^2 60o+cos^2 90o (...

    Text Solution

    |

  10. Evaluate the following: (i) 2sin^2 30o-3cos^2 45o+tan^2 60o (ii) s...

    Text Solution

    |

  11. Evaluate the following: 4(sin^4 60o+cos^4 30o)-3(tan^2 60o-tan^2 4...

    Text Solution

    |

  12. Evaluate the following: cos e c^3 30ocos60otan^3 45osin^2 90osec^2 ...

    Text Solution

    |

  13. Evaluate the following: (cos0o+sin45o+sin30o)(sin90o-cos45o+cos60o)...

    Text Solution

    |

  14. Evaluate the following: (i) 4/(cot^2 30o)+1/(sin^2 60o)-cos^2 45o ...

    Text Solution

    |

  15. Evaluate the following: (tan^2 60o+4cos^2 45o+3sec^2 30o+5cos^2 90o...

    Text Solution

    |

  16. Evaluate the following: (tan45^@)/(cos e c\ 30^@)+(sec60^@)/(cot45^@...

    Text Solution

    |

  17. Find the value of x in each of the following: (i) 2sin3x=sqrt(3) (...

    Text Solution

    |

  18. Find the value of x in each of the following: tanx=sin45ocos45o+...

    Text Solution

    |

  19. If theta=30^@ , verify that: (i) tan2theta=(2tantheta)/(1-tan^2theta...

    Text Solution

    |

  20. If theta=30^@ , verify that: (i) cos2theta=(1-tan^2theta)/(1+tan^2th...

    Text Solution

    |