SAT l l Subject Test : Math l l C question?

If cos x = tan x, which of the following is a possible radian value of x?

SAT l l Subject Test : Math l l C question?
If cos x = tan x, then cos x ≠ 0, so we can multiply through by cos x to get





cos² x = sin x,





and since sin² x + cos² x = 1, we can substitute for sin² x to get





1 - sin² x = sin x ⇒ sin² x + sin x - 1 = 0





⇒ sin x = [ - 1 ± √(1 + 4) ] / 2,





and since | sin x | %26lt; 1, we can conclude that





sin x = [ - 1 + √5 ] / 2.





Proceed from there by using your calculator to find suitable values of x.