tan34/ 2(1-tan34)

Question

tan34/2(1-tan34)

=(2/2)[tan34/2(1-tan34)

=2tan34/4(1-tan34)

i need to have the form 2tanA/1-tan^2A but i cant eliminate the 4

Answer 1

This question utilizes the double angle identity for tangent. This identity states that tan(2θ)=2tan(θ)/(1-tan²θ)

In this situation, our θ=34, and it is a perfect match on the top and bottom of the expression, giving us the freedom to use the double angle identity without too much manipulation.

We start at tan(34)/2(tan²(34))

To make this expression closer to our double angle identity, let's pull the "2" in the denominator to the front, turning it into

1(tan(34))

_____________ , now we can sub the double angle equivalent into the brackets

2(1-tan²(34))

(1/2)[tan(2x34)/2], we multiply the 2s in the denominator together (2x2 is 4), and the θ terms together (2x34=68), which gets us the final answer

tan(68)/4≈0.6188