Let us find the general solutions of cos x = 0.
Now cos-1 0 = π/2
Hence the general solution is
x = ±π/2 + 2kπ, where k is any integer.
Let us find the general solutions of tan x = 0.
Now 
Hence the general solution is
x = kπ, where k is any integer.
Let us find the general solutions of 
.
The equation is equivalent to 
.
Now 
Hence the general solution is
x = π/4 +2kπ or x = 3π/4 +2kπ, where k is any integer.
Let us find the general solutions of sin x = cos x.
The equation is equivalent to 
, which can be simplified to 
.
Now 
Hence the general solution is
x = π/4 +kπ, where k is any integer.
The equation is equivalent to 2cos2x − cos x = 0 which can be factorised to cos x(2cos x – 1) = 0
If cos x = 0, then consider cos-1(0)= π/2.
Hence a solution is x = ±π/2 + 2kπ
If 2cos x – 1 = 0, this equation is equivalent to
Now
Hence a solution is x = ± π/3 + 2kπ
Therefore the general solution is
x = ±π/3 +2kπ or x = ±π/2 +2kπ, where k is any integer.
Let us find the general solutions of 2sin x = -1.
The equation is equivalent to 
.
Now 
and also -5π/6. Hence the general solution is
x = -π/6 +2kπ or x = -5π/6 +2kπ, where k is any integer.