Home
Class 10
MATHS
Prove the following: sinthetasin(90^0-th...

Prove the following: `sinthetasin(90^0-theta)-costhetacos(90^0-theta)=0`

Text Solution

Verified by Experts

`sin(90^@−θ)=cosθandcos(90^@−θ)=sinθ`
L.H.S`=sinθ sin(90^@−θ)−cosθ cos(90^@−θ)`
`=sinθ cosθ−cosθ sinθ`
=0=R.H.S
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

Prove the following: sin theta sin(90^(@)-theta)-cos theta cos(90^(@)-theta)=0

Without using trigonometric tables, evaluate each of the following: (-tanthetacot(90^0-theta)+secthetacos e c(90^0-theta)+sin^2 35^0+sin^2 55^0)/(tan10^0tan20^0tan30^0tan70^0tan80^0)

sin theta cos(90^@ -theta) +cos theta sin(90^@ -theta) = ?

sin theta cos(90^(@)-theta)+cos theta sin(90^(@)-theta)

Prove that :(sin theta cos(90^(0)-theta)cos theta)/(sin(90^(0)-theta))+(cos theta sin(90^(0)-theta)sin theta)/(cos(90^(@)-theta))=1csc^(2)(90^(@)-theta)-tan^(2)theta=cos^(2)(90^(@)-theta)+cos^(2)theta

Without using trigonometrical tables; prove (sin theta)/(sin(90-theta))+(cos theta)/(cos(90^(@)-theta))=sec theta*cosec theta

Evaluate sinthetacos(90^(@)-theta)+costhetasin(90^(@)-theta) .

Find x from the following equation: cos ec(90^(0)+theta)+x cos theta cot(90^(0)+theta)=sin(90^(@)+D)=0

Find the value of costhetacos(90^(@)-theta)-sinthetasin(90^(@)-theta)

Prove the following: (cos(90^(@)-theta)sec(90^(@)-theta)tan theta)/(cos ec(90^(@)-theta)sin(90^(@)-theta)cot(90^(@)-theta))+(tan(90^(@)-theta))/(cot theta)=2

RD SHARMA-TRIGONOMETRIC RATIOS-All Questions
  1. The value of (cos(90^0-theta)sec(90^0-theta)tantheta)/(cos e c(90^0-t...

    Text Solution

    |

  2. If tan2A=cot(A-18^0), where 2A is an acute angle, find the value of A.

    Text Solution

    |

  3. Prove the following: sinthetasin(90^0-theta)-costhetacos(90^0-theta)=0

    Text Solution

    |

  4. Find an acute angle theta , when (costheta-sintheta)/(costheta+sinthet...

    Text Solution

    |

  5. If sin(A+B)=1 and cos(A-B)=(sqrt(3))/2, then find A and B dot

    Text Solution

    |

  6. Evaluate each of the following: cot 12^0cot 38^0cot52^0cot60^0cot78^0 ...

    Text Solution

    |

  7. Prove that: tan10^0tan15^0tan75^0tan80^0=1 tan1^0tan2^0tan3^0tan89^0=...

    Text Solution

    |

  8. If A+B=90^0, prove that sqrt((tanAtanB+tanAcotB)/(sinAsecB)-(sin^2B)/(...

    Text Solution

    |

  9. If sin5theta=cos4theta, whre 5thetaa n d4theta are acute angles, find ...

    Text Solution

    |

  10. If tantheta+1/(tantheta)=2 , find the value of tan^2theta+1/(tan^2thet...

    Text Solution

    |

  11. Evaluate each of the following in the simplest form: cos e c30^0+cot45...

    Text Solution

    |

  12. In a right triangle B C , right angled at B , the ratio of A BtoA C is...

    Text Solution

    |

  13. In Figure, A D=D B \ and \ /B is a right angle. Determine. (a)\ sin th...

    Text Solution

    |

  14. Find the value of x in each of the following: (i)tan3x=sin45^0cos45^...

    Text Solution

    |

  15. If theta is an acute angle and tantheta+cottheta=2, find the value o...

    Text Solution

    |

  16. Prove that: (cos30^0+sin60^0)/(1+cos60^0+sin30^0)=(sqrt(3))/2

    Text Solution

    |

  17. Find the value of theta in each of the following: (i)2sin2theta=sqrt...

    Text Solution

    |

  18. An equilateral triangle is inscribed in a circle of radius 6 cm. Find ...

    Text Solution

    |

  19. If tanA=1 and tanB=sqrt(3),e v a l u a t ecosAcosB-sinAsinBdot

    Text Solution

    |

  20. Find(sin18^0)/(cos72^0)+(sin22^0)/(cos68^0)-(cos38^0cos e c52^0)/(tan1...

    Text Solution

    |