Home
Class 11
MATHS
If acostheta+b sintheta=x and asinthet...

If `acostheta+b sintheta=x` and ` asintheta-bcostheta=y` prove that `a^2+b^2=x^2+y^2`

Text Solution

Verified by Experts

`x = asinθ + bcosθ`
Squaring both sides we get,
`x2 = (asinθ + bcosθ)2 x2 = a2sin2θ + 2(ab)sinθcosθ + b2cos2θ ………. ( 1 )`
`y = acosθ – bsinθ` ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

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

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

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

If x=a cos theta-b sin theta and y=a sin theta+b cos theta then prove that :x^(2)+y^(2)=a^(2)+b^(2)

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

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

If (x)/(a)cos theta+(y)/(b)sin theta=1 and (x)/(a)sin theta-(y)/(b)cos theta=-1, prove that (x^(2))/(a^(2))+(y^(2))/(b^(2))=2

If x/acostheta+y/bsintheta=1,x/asintheta-y/bcostheta=1 , then eliminate theta .

If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove that " x^(2)+y^(2)=a^(2)+b^(2).

If (x)/(a)cos theta+(y)/(b)sin theta=1 and (x)/(a)sin theta-(y)/(b)cos theta=1 Prove that :(x^(2))/(a^(2))+(y^(2))/(b^(2))=2

RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove the following identity: (t a ntheta+s e ctheta-1)/(t a ntheta-s ...

    Text Solution

    |

  2. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

    Text Solution

    |

  3. If acostheta+b sintheta=x and asintheta-bcostheta=y prove that a^2+...

    Text Solution

    |

  4. If tan theta +sin theta =m and tan theta -sin theta =n then prove m^2-...

    Text Solution

    |

  5. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

    Text Solution

    |

  6. Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

    Text Solution

    |

  7. Prove the following identity: (cosec theta - sin theta)(sec theta-cos ...

    Text Solution

    |

  8. Prove the following identity: cos e c\ theta(s e ctheta-1)-cottheta(1-...

    Text Solution

    |

  9. Prove the following identity: (1-s in AcosA)/(cos A(s e c A-cos e c A)...

    Text Solution

    |

  10. Prove the following identity: (t a n A)/(1-cot A)+(cot A)/(1-t a n A)=...

    Text Solution

    |

  11. Prove the following identity: (sin^3A+cos^3A)/(sinA+cosA)+(sin^3A-cos^...

    Text Solution

    |

  12. Prove the following identity: (secA secB + tanA tanB)^2 - (secA tanB+ ...

    Text Solution

    |

  13. Prove the following identity: (costheta)/(1-sintheta)=(1+costheta+sint...

    Text Solution

    |

  14. Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)...

    Text Solution

    |

  15. If (ax)/(costheta)+(by)/(sintheta)=a^2-b^2 , and (axsintheta)/(cos^2th...

    Text Solution

    |

  16. Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2t...

    Text Solution

    |

  17. Prove the following identity: (1+t a nalphat a nbeta)^2+(tanalpha-t a...

    Text Solution

    |

  18. Prove the following identity: ((1+cottheta+t a ntheta)(sin theta-costh...

    Text Solution

    |

  19. Prove the following identity: (2sinthetacostheta-costheta)/(1-sintheta...

    Text Solution

    |

  20. Prove the following identity: costheta(t a ntheta+2)(2t a ntheta+1)=2s...

    Text Solution

    |