Home
Class 10
MATHS
i) If acostheta+bsintheta=m and asinthet...

i) If `acostheta+bsintheta=m` and `asintheta-bcostheta=n`, then prove that: `a^(2)+b^(2)=m^(2)+n^(2)`
ii) If `xsin^(3)theta+ycos^(3)theta=sinthetacostheta` and `xsintheta=ycostheta`, then prove that: `x^(2)+y^(2)=1`

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS|10 Videos

  • INTRODUCTION TO TRIGONOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise PRACTICS-TEST (SECTION-A)|4 Videos

  • INTRODUCTION TO TRIGONOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise SHORT ANSWER TYPE (I) QUESTIONS|15 Videos

  • CONSTRUCTIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise (PRACTICE-TEST) SECTION-C|1 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    CBSE COMPLEMENTARY MATERIAL|Exercise PRACTICE-TEST (SECTION-D)|1 Videos

Similar Questions

Explore conceptually related problems

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

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, prove that a^(2)+b^(2)=m^(2)+n^(2)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, 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 then 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 xsintheta+ycostheta=sintheta.costheta and xsintheta-ycostheta=0 find x^(2)+y^(2)

If cos ec theta-sin theta=I and sec theta-cos theta=m then prove that I^(2)m^(2)(I^(2)+m^(2)+3)=1

If cos ec theta-sin theta=a^(3) and sec theta-cos theta=b^(3) then prove that a^(2)b^(2)(a^(2)+b^(2))=1

If x=cosec theta-sin theta and y=sec theta-cos theta then prove that x^(2/3)+y^(2/3)=(xy)^(-2/3)

If cos ec theta-sin theta=a^(3),sec theta-cos theta=b^(3) then prove that a^(2)b^(2)(a^(2)+b^(2))=1

CBSE COMPLEMENTARY MATERIAL-INTRODUCTION TO TRIGONOMETRY-SHORT ANSWER TYPE QUESTIONS
  1. (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA)

    Text Solution

    |

  2. Prove 1/(secx-tanx)-1/(cosx)=1/(cosx)-1/(secx+tanx)

    Text Solution

    |

  3. (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+tantheta+cottheta=se...

    Text Solution

    |

  4. Prove that (sin theta + "cosec" theta)^(2)+(cos theta + sec theta)^(...

    Text Solution

    |

  5. secA(1-sinA)(secA+tanA)=1

    Text Solution

    |

  6. If tantheta+sintheta=m and tantheta-sintheta=n, then prove that: m^(2)...

    Text Solution

    |

  7. If sectheta=x+(1)/(4x),prove that sectheta+tantheta=2xor(1)/(2x)*

    Text Solution

    |

  8. If sintheta+sin^2theta=1 , prove that cos^2theta+cos^4theta=1

    Text Solution

    |

  9. Without using trigonometric table, the value of cotthetatan(90^(@)-t...

    Text Solution

    |

  10. Prove that : (cot(90^(@)-theta))/(tantheta)+("cosec"(90^(@)-theta)sint...

    Text Solution

    |

  11. Without using trigonometric tables, evaluate each of the following: (...

    Text Solution

    |

  12. If A, B, C are the angles of DeltaABC then prove that "cosec"^(2)((B+C...

    Text Solution

    |

  13. Find the value of sec^(2)10^(@)-cot^(2)80^(@)+(sin15^(@)cos75^(@)+cos1...

    Text Solution

    |

  14. Prove the following identities: (tantheta-cottheta)/(sinthetacostheta...

    Text Solution

    |

  15. If sintheta+costheta=sqrt2costhetathen costheta-sintheta is equal to

    Text Solution

    |

  16. Evaulate : 4-(sin30^(@)+tan45^(@)-"cosec"60^(@))/(sec30^(@)+cos60^(@)+...

    Text Solution

    |

  17. Prove that : 1-(sinAsin(90^(@)-A))/(cot(90^(@)-A))=sin^(2)A

    Text Solution

    |

  18. i) If acostheta+bsintheta=m and asintheta-bcostheta=n, then prove that...

    Text Solution

    |

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

    Text Solution

    |

  20. Without using trigonometric tables, evaluate each of the following: (...

    Text Solution

    |