Answer:
Step-by-step explanation:
Use the sum of angle formula:
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
This gives you ...
cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)
Subtracting the right-side trig function terms and factoring, we have ...
cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1
Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...
cos(x)·0 -sin(x)(-2sin(π/6)) = 1
sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1
x = arcsin(1)
x = π/2
_____
When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.
