Question

if sinA+cosA=1 then prove that cosA-sinA=+-1​

Answer 1

Step-by-step explanation:

sinA+CosA=1(given)--1

Sq both sides

(sinA+cosA)^2=

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

1+2sinAcosA=1

2sinAcosA=0

sinAcosA=0

sinA=0

Now substituting sinA's value

0+cosA=1

cosA=1

Case 1

sinA=0

cosA=1

Let an equation sinA-cosA

0-1=-1

sinA-cosA=-1

Now taking the same equation

sinAcosA=0

cosA=0 and thus by substituting in 1 we get sinA=1

Case 2

sinA=1

cosA=0

Let us take equation sinA-cosA

1-0=1

sinA-cosA=1