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`sintheta+costheta=sqrt(2)`

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To solve the equation \( \sin \theta + \cos \theta = \sqrt{2} \), we can follow these steps: ### Step 1: Multiply both sides by \( \sqrt{2} \) We start with the equation: \[ \sin \theta + \cos \theta = \sqrt{2} \] Multiplying both sides by \( \sqrt{2} \): ...
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sintheta+costheta=(sqrt(3)+1)/(2)

If costheta-sintheta=sqrt(2)sintheta , then prove that: costheta+sintheta=sqrt(2)costheta

Knowledge Check

  • If sin theta+costheta=sqrt(2)costheta then what is (costheta-sintheta) equal to ?

    A
    `-sqrt(2)costheta`
    B
    `-sqrt(2)sintheta`
    C
    `sqrt(2)sintheta`
    D
    `2sin theta`
  • Evaluate sintheta times costheta if sintheta+costheta=sqrt2

    A
    `sqrt2`
    B
    1
    C
    0
    D
    `(1)/(2)`
  • Let P={theta:sintheta-costheta=sqrt2costheta}and Q={theta: sintheta+costheta=sqrt2sintheta} be two sets. Then

    A
    `psubQ and Q-P=phi`
    B
    `QcancelsubP`
    C
    `PcancelsubQ`
    D
    P=Q
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