Posted by john 2020 on Friday, March 19, 2010 at 12:28am.
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
x = π + π/4 = 5π/4 or
x = 2π - π/4 = 7π/4
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
Related Questions
trig - Solve cos x-1 = sin^2 x Find all solutions on the interval [0,2pi) a. x=...
math - Eliminate the parameter (What does that mean?) and write a rectangular ...
Trig - Solve the equation on the interval 0 less than or equal 0 < 2pi. 1...
precalc/trig - olve for the interval [0, 2pi]. cos(x+ pi/4)+cos(x- pi/4)=1
calculus - pleaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaasw help can you ...
math - Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the ...
calculus - Let g(x)=|cos x-1|. The maximum value attained by g on the closed ...
Precalculs - I have no idea how to do these type of problems. -------Problem...
Pre-Calculus - cos^2(x) + sin(x) = 1 - Find all solutions in the interval [0, ...
Calculus - Find the interval(s) where the function is increasing where and it is...
For Further Reading
