to answer the question above, take the LHS.
[(tan x - 1) / (tan x + 1)] =
Remember that tan x = 1 / cot x.
{[(1 / cot x) - 1] / [(1 / cot x) + 1]} =
The LCD is cot x. Multiply as needed to get the common denominator for all terms.
{[(1 / cot x) - 1(cot x / cot x)] / [(1 / cot x) + 1(cot x / cot x)]} =
{[(1 / cot x) - (cot x / cot x)] / [(1 / cot x) + (cot x / cot x)]} =
Then Simplify.
[(1 - cot x) / cot x] / [(1 + cot x) / cot x] =
Remember that (a / b) / (c / d) = (a / b) * (d / c).
[(1 - cot x) / cot x] * [cot x / (1 + cot x)] =
[(1 - cot x) / (1 + cot x )] =
RHS
The answer is
[(tan x - 1) / (tan x + 1)] = [(1 - cot x) / (1 + cot x )]
