Posted by **john 2020** on Friday, March 19, 2010 at 12:28am.

solve the equation on the interval [0,2pi)

cos(x+pi/4)-cos(x-pi/4)=1

- precal -
**Reiny**, Friday, March 19, 2010 at 8:04am
first expand it

cosxcosπ/4 - sinxsinπ/4 - (cosxcoxπ/4 + sinxsinπ/4) = 1

-2sinxsinπ/4 = 1

-2sinx(√2/2) = 1 , since we know sinπ/4 = 1/√2 or √2/2

sinx = -1/√2

the sine is negative in III and IV

so

x = π + π/4 = **5π/4</b? or
**

x = 2π - π/4 = **7π/4**

- check typing - precal -
**Reiny**, Friday, March 19, 2010 at 8:07am
x = π + π/4 = 5π/4 or

x = 2π - π/4 = 7π/4

- precal -
**drwls**, Friday, March 19, 2010 at 8:10am
Use the identity formulas for cos(a+b) and cos(a-b):

cosx*cos(pi/4) - sinx*sin(pi/4)-cosx*cos(pi/4) - sinx*sin(pi/4) = 1

-2 sinx*sin(pi/4)= 1

sinx (1/sqrt2)= -1/2

sinx = -(sqrt2)/2

x = 5 pi/4 or 7 pi/4

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