Question

How do you simplify `sec xcos (frac{\pi}{2} - x )`?

Answer 1

The application of co-functions will make it easy to simplify this expression.

However, I am going to present how the co-function is derived so you can have a better understanding as to why it came as such.

The co-function of `cos (pi/2) -x` is `sin x`

So how did this happen?

Examine the following equation

`cos ( A- B) = cos A * cos B + sin A * sin B`

Thus, applying this formula to `cos (pi/2) -x`

`cos (pi/2) -x = cos (pi/2) * cos x + sin (pi/2) * sinx`

`cos (pi/2) = 0 and sin (pi/2) = 1`

therefore,

`cos [(pi/2) -x] = sin x`

Thus,

`sec x *sin x`

but,

`sec x = 1/cosx`

then

`1/cosx * sin x`

`tan x`