Question

if (CosA+SinA)=1,prove that(CosA-SonA)=1

Answer 1

The solution for the given question,
"If CosA-SinA=1, Prove that CosA+SinA=+_1"
is-

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Answer 2

Hey friend!!

Here's ur answer...


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$\\ \\ we \: know \: that \: \\ \\ \\ { \sin }^{2} (a) + { \cos }^{2} = 1 \\ \\ given \: \\ \sin(a) + \cos(a) = 1 \\ \\ squaring \: both \: sides \: \\ \\ ( \sin(a) + \cos(a) {)}^{2} = {1}^{2} \\ { \sin }^{2}(a) + { \cos }^{2} (a) + 2 \sin(a) . \cos(a) = 1 \\ 1 + 2 \sin(a) . \cos(a) = 1 \\ 2 \sin(a) . \cos(a) = 0 \\ \sin(a) . \cos(a) = 0 \: - - - - - (1) \\ \\ \\ now \: taking \: \\ \\ ( \sin(a) - \cos(a) {)}^{2} = { \sin }^{2} (a) + { \cos }^{2} (a) - 2 \sin(a) . \cos(a) \\ ( \sin(a) - \cos(a) {)}^{2} \: = 1 - 0 \\ \sin(a) - \cos(a) = \sqrt{1} = 1 \\ \\ hence \: proved.$


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