Question

Solve the given equation

cos(θ) − sin(θ) = 1


I got the answer to be 3pie/2 and 0 but its wrong can someone help Thank you

Answer 1

cos(?) ? sin(?) = 1 , I will assume Ø from 0 to 2?

cosØ = 1+sinØ
square both sides
cos^2 Ø = 1 + 2sinØ + sin^2 Ø
1 - sin^2 Ø = 1 + 2sinØ + sin^2 Ø
2sin^2 Ø + 2sinØ = 0
2sinØ(sinØ + 1) = 0
sinØ = 0 or sinØ = -1

Ø = 0, ?, 2?
or
Ø = 3?/2

BUT, since I squared , all answers must be verified in the original equation

Ø = 0
LS = cos0 - sin0 = 1-0 = 1
RS = 1 , so Ø = 0
Ø = ?
LS = cos? - sin? = -1 - 0 = -1 ? RS, so Ø ? ?
Ø = 2?
LS = cos 2? - sin 2? = 1 - 0 = 1 = RS, so Ø = 2?
Ø = 3?/2
LS = cos 3?/2 - sin 3?/2 = 0 - (-1) = 1 = RS

Ø = 0, 3?/2, and 2?

check with Wolfram:
http://www.wolframalpha.com/input/?i=cos(x)+%E2%88%92+sin(x)+%3D+1+from+-0.5+to+6.5