How to Simplify an Expression Using Cofunction Identities
If you take the graph of y = sin x and shift it to the left by pi/2 units, it looks exactly like the graph of y = cos x. The same is true for tangent and cotangent, as well as secant and cosecant. That’s the basic premise of cofunction identities — they say that the sine and cosine functions take on the same values, but those values are shifted slightly on the coordinate plane when you look at one function compared to the other.
Here is a list of cofunction identities:
The cofunction identities are great to use whenever you see pi/2 inside the grouping parentheses. You may see functions in the expressions such as
If the quantity inside the trig function looks like
you’ll know to use the cofunction identities.
For example, to simplify
follow these steps:

Look for cofunction identities and substitute.
First realize that cos(pi/2 – x) is the same as sin x because of the cofunction identity. That means you can substitute sin x in for cos(pi/2 – x) to get

Look for other substitutions you can make.
Because of the reciprocal identity for cotangent,
is the same as cot x.