Question

How do you prove (cos x + cot x) / (tan x + sin x) = cot x csc x?

Answer 1

To prove the given identity (cos x + cot x) / (tan x + sin x) = cot x csc x, we express cot x and csc x in terms of sine and cosine, substitute these expressions into the left-hand side of the equation, and simplify the expression to show that it equals cot x csc x.

Step-by-step explanation:

To prove the given identity:

(cos x + cot x) / (tan x + sin x) = cot x csc x

First, let's express cot x and csc x in terms of sine and cosine:

cot x = cos x / sin x

csc x = 1 / sin x

Now, substitute these expressions into the left-hand side of the equation:

(cos x + cos x / sin x) / (sin x + sin x) = (2cos x) / (2sin x) = cot x csc x