Establish the following identity

tan(x+pi/4)=1+tanx/1-tanx

Use the tan (x + y) formula.

tan(x+y) = (tanx + tany)/(1 - tanx tany)

with y = pi/4, tany = 1

Your right hand side should have parentheses

To establish the given trigonometric identity, we can use the properties and definitions of trigonometric functions.

Starting with the left-hand side (LHS) of the equation:

tan(x + π/4)

We can express tan(x + π/4) using the trigonometric sum formula:

tan(A + B) = (tanA + tanB) / (1 - tanA * tanB)

Let A = x and B = π/4:

tan(x + π/4) = (tanx + tan(π/4)) / (1 - tanx * tan(π/4))

Now, we need to evaluate tan(π/4).

Since tan(π/4) represents the tangent of 45 degrees, we know that it is equal to 1.

Plugging this value back into the equation:

tan(x + π/4) = (tanx + 1) / (1 - tanx * 1)

Simplifying further:

tan(x + π/4) = (tanx + 1) / (1 - tanx)

This matches the right-hand side (RHS) of the given equation:

1 + tanx / (1 - tanx)

Therefore, the identity tan(x + π/4) = 1 + tanx / (1 - tanx) is true.