Question

if cos a -sin a =1 prove that cos a + sin a =+-1.

Answer 1

sq. on both side

( cos a - sin a)^2 = (1)^2
cos^2 a +sin ^2 a - 2 sina cos a = 1
1 - 2 sin a cos a =1
1-1 = 2 sin a cos a
0 = sin a cos a. ......(1)

(cos a - sin a )^2 = 1
acos ^2 + asin ^2 - 2 sina cos a = 1
add 4 sina cos a both side

a cos ^2 + a sin ^2 - 2sina cos a + 4 sin acos = 1 + 4 sin a cos a
( cos a + sin a) ^2 = 1 -4(0) ....from eq. 1
cos a + sin a= +-1