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Solve sin theta+cos theta=sqrt(2) cos A....

Solve `sin theta+cos theta=sqrt(2) cos A`.

Text Solution

Verified by Experts

The correct Answer is:
`theta=2n pi +pi/4 pm A, n in Z`
`sin theta + cos theta=sqrt(2) cos A`
`rArr (1//sqrt(2)) sin theta +(1//sqrt(2)) cos theta=cos A`
or `cos (theta-pi//4)=cos A`
`rArr theta-pi//4=2npi pm A`
or `theta=2npi+pi//4 pm A, AA n in Z`
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Knowledge Check

  • 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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