Home
Class 10
MATHS
If acostheta-bsintheta=c, then prove tha...

If `acostheta-bsintheta=c`, then prove that:
`asintheta+bcostheta=+-sqrt(a^(2)+b^(2)-c^(2))`

Text Solution

Verified by Experts

Given ` a cos theta- b sin theta=c`
squaring both sides
`a^2cos^2 theta + b^2 sin^2 theta-2 ab sin theta cos theta=c^2`
`a^2-a^2sin^2 theta + b^2-b^2 cos^2 theta - 2ab sin theta cos theta=c^2`
...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    RD SHARMA|Exercise All Questions|361 Videos

  • TRIGONOMETRIC RATIOS

    RD SHARMA|Exercise All Questions|249 Videos

Similar Questions

Explore conceptually related problems

If a cos theta-b sin theta=c; prove that a sin theta+b cos theta=+-sqrt(a^(2)+b^(2)-c^(2))

If a cos theta - b sin theta =c , then prove that a sin theta + b cos theta = +- sqrt(a^(2) + b^(2) - c^(2))

If a sin theta+b cos theta=c then prove that a cos theta-b sin theta=sqrt(a^(2)+b^(2)-c^(2))

If a cos theta - b sin theta = c, prove that a sin theta + b cos theta = pm sqrt(a^(2) + b^(2) - c^(2)) .

Ifa sin theta+b cos theta=C, then prove that a cos theta-b sin theta=sqrt(a^(2)+b^(2)-c^(2))

i) If acostheta+bsintheta=m and asintheta-bcostheta=n , then prove that: a^(2)+b^(2)=m^(2)+n^(2)

If acostheta+bsintheta=m and asintheta-bcostheta=n , then show that a^(2)+b^(2)=m^(2)+n^(2) .

If asintheta+bcostheta=c , then acostheta-b sintheta is equal to

If x=acostheta-bsinthetaandy=asintheta+bcostheta , then show that : x^(2)+y^(2)=a^(2)+b^(2)

If asintheta+bcostheta=c , find acostheta-bsintheta=?

RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. If sintheta+sin^2theta+sin^3theta=1, then prove that cos^6theta-4cos^4...

    Text Solution

    |

  2. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

    Text Solution

    |

  3. If acostheta-bsintheta=c, then prove that: asintheta+bcostheta=+-sqr...

    Text Solution

    |

  4. Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+s...

    Text Solution

    |

  5. Prove the following identities: (sintheta)/(1-costheta)+(tantheta)/(1...

    Text Solution

    |

  6. Find (1 + tantheta + sectheta)(1+ cottheta - cosectheta)

    Text Solution

    |

  7. Prove the following identities: 1/(cos e cA-cotA)-1/(sinA)=1/(sinA)-1/...

    Text Solution

    |

  8. Prove the following trigonometric identities: (sintheta)/(1-costheta)=...

    Text Solution

    |

  9. Prove the following trigonometric identities: sqrt((1-sintheta)/(1+sin...

    Text Solution

    |

  10. Prove the following identities: (1-sintheta)/(1+sintheta)= (sectheta...

    Text Solution

    |

  11. If cos e ctheta-sintheta=l and sectheta-costheta=m , prove that l^2m^2...

    Text Solution

    |

  12. If tanA=ntanB and sinA=msinB, prove that cos^2A=[m^2-1]/[n^2-1]

    Text Solution

    |

  13. If x=asinthetaa n dy=btantheta, then prove that (a^2)/(x^2)-(b^2)/(y^2...

    Text Solution

    |

  14. If (cosalpha)/(cosbeta)=m and (cosalpha)/(sinbeta)=n show that (m^2+n^...

    Text Solution

    |

  15. Prove the following identities: cos^4A-cos^2A=sin^4A-sin^2A

    Text Solution

    |

  16. Prove the following identities: (sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/...

    Text Solution

    |

  17. If xsin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta, p...

    Text Solution

    |

  18. If cos e ctheta-sintheta=m and sectheta-costheta=n , prove that (m^...

    Text Solution

    |

  19. Prove the following identities: (cosA)/(1-tanA)+(sin^2A)/(sinA-cosA)=...

    Text Solution

    |

  20. Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(co...

    Text Solution

    |