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.