Problem

18. Simplify: $\frac{2 \tan x}{1+\tan ^{2} x}$

Answer

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Answer

\(\boxed{\frac{2 \tan x}{\sec^2 x}}\)

Steps

Step 1 ：Given expression: \(\frac{2 \tan x}{1+\tan ^{2} x}\)

Step 2 ：Use the identity: \(\tan^2 x + 1 = \sec^2 x\)

Step 3 ：Replace \(\tan^2 x\) with \(\sec^2 x - 1\): \(\frac{2 \tan x}{\sec^2 x - 1 + 1}\)

Step 4 ：Simplify the expression: \(\frac{2 \tan x}{\sec^2 x}\)

Step 5 ：\(\boxed{\frac{2 \tan x}{\sec^2 x}}\)

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