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Prove that the general solution of tanth...

Prove that the general solution of `tantheta=tanalpha` is given by : `theta=npi+alpha,n in Zdot`

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Given:
`tantheta=tanalpha`
`implies sintheta/costheta=sinalpha/cosalpha`
`implies sintheta/costheta-sinalpha/cosalpha=0`
Taking LCM
`implies(sinthetacosalpha-costhetasinalpha)/(costhetacosalpha)=0`
`implies sin(theta-alpha)/(costhetacosalpha)=0`
`implies sin(theta-alpha)=0`
`theta-alpha=npi` where, `npi in Z`
i.e. `n=(0,pm1,pm 2,pm 3---)`
`theta=npi+alpha`
Hence the general solution of `tantheta=tanalpha` is `theta=npi+alpha` where `n in Z`
i.e. `n=(0,pm 1, pm 2, pm 3,----)`
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Knowledge Check

  • Find the general solution of equation tan theta = cot alpha .

    A
    `theta = n pi + (pi)/(2) - alpha`
    B
    `theta = n pi + alpha`
    C
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    D
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    C
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  • General solution of tantheta+tan((pi)/(2)-theta)=2 is

    A
    `npi+(pi)/(8), ninZ`
    B
    `2npi+(pi)/(8), ninZ`
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