Question

If cos A - sin A = 1 Prove that cos A sin A = 1 or -1

Answer 1

I think your question is incorrect

cosA-sinA=1

squaring on both sides

cos^2A+sin^2A-2sinAcosA=1......eq1

as we know

sin^2A+cos^2A=1

so

1-2sinAcosA=1

0=2sinAcosA

sinAcosA=0

ok

let sinAcosA=1

then

from eq1

we get sin^2A+cos^2A=3

which is not possible

and if we let sinAcosA=-1

then from eq1

we get

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

which is not possible

so question should be

if cos A - sin A = 1 Prove that cos A sin A = 0

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