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!