# If sin A- cos A=1 then prove that sin A+ cos A =plus minus 1?

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Noah G
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Feb 9, 2018

Squaring both sides:

#(sinA- cosA)^2 = 1^2#

#sin^2A - 2sinAcosA + cos^2A = 1#

#1 - 2sinAcosA = 1#

#0 = 2sinAcosA#

#0 = sin(2A)#

Now if we repeat the same thing with

#(sinA + cosA)^2 = B^2#

#sin^2A + cos^2A + 2sinAcosA= B^2#

#sin(2A) = B^2 - 1#

From the above step, recall that

#0 = B^2 - 1#

#0 = (B + 1)(B - 1)#

#B = 1 or -1#

Therefore,

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dk_ch
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Feb 9, 2018

Using formula

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