Question

Question #92f06

Answer 1

`x = pi/2, and x = pi`

Explanation:

use trig identity;
`sin x - cos x = - sqrt2cos (x + pi/4)`
In this case:
`- sqrt2cos (x + pi/4) = 1`
`cos (x + pi/4) = -1/sqrt2 = -sqrt2/2`
Trig table and unit circle give 2 solutions:
(`x + pi /4) =+- (3pi)/4`

a. `x = (3pi)/4 - pi/4 = (2pi)/4 = pi/2`
b. `x + pi/4 = - ((3pi)/4)`, or `x + pi/4 = (5pi)/4` (co-terminal)
`x = ((5pi)/4) - pi/4 = (4pi)/4 = pi`
Check.
When `x = pi/2` --> sin x = 1 --> cos x = 0
sin x - cos x = 1 - 0 = 1. Proved.
When `x = pi` --> sin x = 0 --> cos x = - 1
sin x - cos x = 0 - (- 1) = 1. Proved.