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If t a ntheta+sintheta=m and tantheta-si...

If `t a ntheta+sintheta=m` and `tantheta-sintheta=n ,` show `m^(2-)n^2=4sqrt(m ndot)`

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To prove that \( m^2 - n^2 = 4 \sqrt{mn} \) given the equations \( m = \tan \theta + \sin \theta \) and \( n = \tan \theta - \sin \theta \), we will follow these steps: ### Step 1: Write down the expressions for \( m \) and \( n \) We have: \[ m = \tan \theta + \sin \theta \] \[ ...
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Explore conceptually related problems

If tan theta+sin theta=m and tan theta-sin theta=n show that m^(2)-n^(2)=4sqrt(nm)

If tantheta+sintheta=m and tantheta-sintheta=n , then prove that: m^(2)-n^(2)=4sqrt(mn)

Knowledge Check

  • If tantheta+sintheta=mandtantheta-sintheta=n ,then

    A
    `m^2-n^2=4mn`
    B
    `m^2+n^2=4mn`
    C
    `m^2-n^2=m^2+n^2`
    D
    `m^2-n^2=4sqrt(mn)`

  • If tantheta+sintheta=m and tantheta-sintheta=n , then the value of m^2-n^2 is equal to (a)4 mn (b) 2sqrt(mn) (c) 4sqrt(mn) (d) 2sqrt(m//n)

    A
    4 mn
    B
    `2sqrt(mn)`
    C
    `4sqrt(mn)`
    D
    `2sqrt(m//n)`

  • If tantheta+sintheta=m and tan theta-sin theta=n , then find the value of m^(2)-n^(2) .

    A
    a) `sqrt(mn)`
    B
    b) `2sqrt(mn)`
    C
    c) `3sqrt(mn)`
    D
    d) `4sqrt(mn)`

    • Similar Questions

    Explore conceptually related problems

    If tantheta +sintheta = m and tantheta-sintheta=n , then prove that m^(2)-n^(2)=4sinthetatantheta .

    If tan theta+sin theta=m and tan theta-sin theta=n then m^(2)-n^(2)=4mn(b)m^(2)+n^(2)=4mnm^(2)-n^(2)=m^(2)+n^(2)(d)m^(2)-n^(2)=4sqrt(mn)

    sintheta=-1/2 and tantheta=-1/sqrt(3)

    If cottheta(1+sintheta)=4m and cottheta(1-sintheta)=4 n, then prove that: (m^(2)-n^(2))^(2)=mn

    If tantheta+sintheta=mandtantheta-sintheta=n , then find the value of sqrt(mn) .

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