Question

if the cos A -sin A =1 prove that Cos A + sin A=+-1

Answer 1

Cos A + Sin A=1
1 - Sin A - cosA= 0
-SinA - CosA = -1
Sin A + Cos A = + - 1

Answer 2

Hey !!!

CosA - sinA = 1 -----1)

CosA + sinA -----;--2)

1st of all adding equation 1 and 2 we get.

(CosA - sinA )² + (cosA + sinA )²

= Cos²A + sin²A - 2sinA ×cosA + cos²A + sin²A + 2sinA ×cosA

= 1 + 1 = 2

Now , from 1 , there is given that ..

CosA - sinA = 1

So,( cosA - sinA )² + (cosA + sinA )² = 2

=> 1² + (cosA + sinA )² = 2

(CosA + sinA ) =√ 2-1

CosA + SinA =+-√1 Prooved


Hope it helps you !!!!

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