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13 October, 20:36

If cosx+sinx=sqrt (2) cosx then show that cosx-sinx=sqrt (2) sinx

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  1. 13 October, 20:59
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    Hello,

    We suppose cos (x) ≠0 and sin (x) ≠0

    cos (x) + sin (x) = √2 cos (x)

    ==>1+tg (x) = √2

    ==>tg (x) = √2-1

    ==>1/tg (x) = 1 / (√2-1)

    ==>cos (x) / sin (x) = √2+1

    ==>cos (x) = sin (x) + √2*sin (x)

    ==>cos (x) - sin (x) = √2 sin (x)
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