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

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Answer 1 · 2014-12-15T13:04:45

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#