Question

PlEASE HELP FAST.
Given:

cos A - sin A = 1

To Prove:

cos A + sin A = 1

Answer 1

Answer:

Step-by-step explanation: cos a= 1+sin a sqaring on both sides we get cos2 a=1+sin2 a+2sin a.. By further solving we get sin a= cos2 a . And cos a = sin2 a . Substituting these in sin a+cos a we get 1

Answer 2

$We know that, \\ \\ \sin^2A+\cos^2A=1$

$(\cos A - \sin A)^2=1^2 \\ \\ \sin^2A+\cos^2A-2\sin A \cdot \cos A =1 \\ \\ 1-2\sin A \cdot \cos A = 1 \\ \\ -2\sin A \cdot \cos A = 0 \\ \\ -1 \times \ -2\sin A \cdot \cos A = -1 \times 0 \\ \\ 2 \sin A \cdot \cos A=0$

$\sin^2A+\cos^2A=1 \\ \\ \sin^2A+\cos^2A+2\sin A \cdot \cos A=1+2\sin A \cdot \cos A \\ \\ (\sin A + \cos A)^2=1+0 \\ \\ (\sin A + \cos A)^2=1 \\ \\ \sin A + \cos A = \sqrt{1} \\ \\ \sin A + \cos A =\pm 1 \\ \\ \cos A + \sin A = \pm 1$

$Hence proved! \\ \\ Also found that, \ \ \ \cos A + \sin A = -1$

$Hope this helps you. \\ \\ Please trust me that the answer is on my own words and not from any source. \\ \\ Please mark it as the \ \bold{brainliest}.\ \\ \\ Also ask me if you've any doubt. \\ \\ \\ Thank you. :-)$