maths (trigonometry)

if cosx-sinx=root 2 sinx, then what is the value of cosx+sinx. How

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  1. √2sinx + sinx = cosx
    sinx(√2+1)= cosx
    sinx/cosx = 1/(√2+1)
    tanx = 1/(√2+1)

    now construct a right-angled triange with sides 1 and √2+1
    let the hypotenuse be r
    r^2 = 1^2 + (√2+1)^2 = 1 + 2 + 2√2 + 1 = 4 + 2√2
    r = √(4+2√2))

    cosx + sinx = (√2+1)√(4+2√2) + 1/(√(4+2√2)

    = (√2 + 2)/(√(4 + 2√2)

    You might want to rationalize this to get a different looking answer.

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