prove

cosx+cotx/secx+tanx
=cosxcotx

To prove that cosx + cotx / secx + tanx = cosxcotx, we need to simplify the expression on the left-hand side (LHS) and show that it is equal to cosxcotx.

Let's start by simplifying the LHS step by step:

cosx + cotx / secx + tanx

First, we need to calculate the reciprocal of secx and tanx:

Reciprocal of secx = 1 / secx = cosx
Reciprocal of tanx = 1 / tanx = cotx

Now let's substitute these values in the expression:

cosx + cotx / cosx + cotx

Next, we need to express the LHS with the same denominator:

(cosx + cotx) / (cosx + cotx)

Since the numerator and denominator are the same, the expression becomes:

1

So, the LHS is equal to 1, which is not equal to cosxcotx.

Therefore, the given statement cosx + cotx / secx + tanx = cosxcotx is NOT true.

If you have any additional questions, feel free to ask!