Question

Question #5cb4b

Answer 1

Given: `cos(x) - sqrt2/2 = sin(x), 0^@ <= x <= 360^@`

Add `sqrt2/2-sin(x)` to both sides:

`cos(x)-sin(x) = sqrt2/2, 0^@ <= x <= 360^@`

Multiply both sides by `sqrt2/2`

`sqrt2/2cos(x)-sqrt2/2sin(x) = 1/2, 0^@ <= x <= 360^@`

Use the identity `cos(A+B)= cos(A)cos(B)-sin(A)sin(B)` where `A = x` and `B = 45^@` (because sin(45^@) = cos(45^@) = sqrt2/2):

`cos(x+45^@) = 1/2, 0^@ <= x <= 360^@`

`x+45^@ = cos^-1(1/2), 0^@ <= x <= 360^@`

`x +45^@ = 60^@` and `x + 45^@= 300^@`

`x = 15^@` and `x = 255^@`