Home
Class 10
MATHS
If sin theta + cos theta = m and sec th...

If ` sin theta + cos theta = m and sec theta + "cosec" theta = n, ` prove that
` n(m^(2)-1) = 2m. `

Text Solution

Verified by Experts

We have
` n(m^(2) -1) = ( sec theta + "cosec" theta )[( sin theta + cos theta)^(2) -1] `
` = ((1)/(cos theta) + (1)/(sin theta))[(sin^(2)theta + cos^(2)theta) + 2 sin theta cos theta -1 ] `
` =((sin theta + cos theta))/(sin theta cos theta) * 2 sin theta cos theta `
`=2(sin theta + cos theta)= 2m. `
Hence, `n(m^(2) -1) = 2m. `
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13A|38 Videos

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13B|15 Videos

  • TRIANGLES

    RS AGGARWAL|Exercise Test Yourself|20 Videos

  • TRIGONOMETRIC RATIOS

    RS AGGARWAL|Exercise Exercise 10|35 Videos

Similar Questions

Explore conceptually related problems

If sin theta + cos theta = p and sec theta + "cosec"theta = q , then prove that q(p^(2)-1) = 2p .

If sin theta + costheta = m and sin theta - cos theta = n , then

If cot theta + cos theta = m and cot theta - cos theta = n then prove that: m^(2) - n^(2) = 4sqrt(mn)

If cos theta + sin theta = m , sec theta + cosec theta =n , What is m//n ?

If sin theta+cos theta=m and sec theta+cos ec theta=n then n(m+1)(m-1) equals

If sin theta + cosec theta =2, then sin^n theta+"cosec"^n theta is equal to

If (tan theta + sin theta) =m and (tan theta - sin theta) = n , prove that (m^(2)-n^(2))^(2)=16mn.

If "cosec" theta - sin theta = m and sec theta - cos theta = n, then what is m^(4/3) n^(2/3) +m^(2/3) n^(4/3) equal to ?

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)

RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Test Yourself
  1. If sin theta + cos theta = m and sec theta + "cosec" theta = n, prov...

    Text Solution

    |

  2. (cos^(2)56^(@)+cos^(2)34^(@))/(sin^(@)56^(@)+sin^(2)34^(@))+3tan^(2)56...

    Text Solution

    |

  3. (sin^2 30^@ cos^2 45^@+4 tan^2 30^@+1/2 sin^2 90^@+1/8 cot^2 60^@)=?

    Text Solution

    |

  4. If cosA+cos^(2)A=1, then sin^(2)A+sin^(4)A=?.

    Text Solution

    |

  5. If sin theta=(sqrt(3))/(2)" then " ("cosec"theta+cot theta)=?

    Text Solution

    |

  6. If cotA=(4)/(5), then ((sinA+cosA))/((sinA-cosA))=?

    Text Solution

    |

  7. If 2x=secA and (2)/(x)=tanA, " prove that " (x^(2)-(1)/(x^(2)))=(1)/(4...

    Text Solution

    |

  8. If sqrt(3) tantheta=3sintheta, " prove that " (sin^(2)theta-cos^(2)the...

    Text Solution

    |

  9. Prove that ((sin^(2)73^(@)+sin^(2)17^(@)))/((cos^(2)28^(@)+cos^(2)62^(...

    Text Solution

    |

  10. If 2sin2 theta=sqrt(3) ,then the value of theta is :

    Text Solution

    |

  11. Prove that sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).

    Text Solution

    |

  12. If cosec theta + cot theta= p, cos theta = ?

    Text Solution

    |

  13. Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

    Text Solution

    |

  14. If 5cottheta=3. find the value of (5sintheta-3costheta)/(4sintheta+3co...

    Text Solution

    |

  15. Prove that (sin32^(@)cos58^(@)+cos32^(@)sin58^(@))=1.

    Text Solution

    |

  16. If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove t...

    Text Solution

    |

  17. ((1+sintheta))/((1-sintheta))=?

    Text Solution

    |

  18. Prove that (1)/((sec theta - tan theta))-(1)/(cos theta)=(1)/(cos th...

    Text Solution

    |

  19. ((sinA-2sin^(3)A))/((2cos^(3)A-cosA)) = ?

    Text Solution

    |

  20. Prove that (tanA)/((1-cotA))+(cotA)/((1-tanA))=(1+tanA+cotA).

    Text Solution

    |

  21. If sec5A="cosec"(A-36^(@)) and 5A " is an acute angle, show that " A=2...

    Text Solution

    |