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If sin theta + cos theta = sqrt(2), then...

If `sin theta + cos theta = sqrt(2)`, then `tan theta=`

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`sintheta+costheta=sqrt2`
squaring both side
`(sintheta+costheta)^2=2`
`sin^2theta+cos^2theta+2sinthetacostheta=2`
`1+2sinthetacostheta=2`
`2sinthetacostheta=1`
`(2sinthetacostheta)/cos^2theta=1/(cos^2theta)`
`2tantheta=1+tan^2theta`
...
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Knowledge Check

  • If sin theta + cos theta = sqrt(3), tan theta + cot theta = ?

    A
    `(1)/(sqrt(3))`
    B
    `1/2`
    C
    1
    D
    `3/2`

  • If sin theta+ cos theta = sqrt(2) cos theta, (theta ne 90^(@)) then value of tan theta is

    A
    `sqrt(2)-1`
    B
    `sqrt(2)+1`
    C
    `sqrt(2)`
    D
    `-sqrt(2)`

  • If sin theta + cos theta theta = sqrt(2) cos theta then cos theta - sin theta is

    A
    `sqrt(2) cos theta`
    B
    `sqrt(2) sin theta `
    C
    `+- sqrt(2) sin theta `
    D
    `sqrt(2) ( cos theta + sin theta)`

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