Problem

tan⁡2x−tan⁡x1+tan⁡2xtan⁡x=

Answer

Expert–verified
Hide Steps
Answer

tan⁡x(1+tan2⁡x)1+tan2⁡x=tan⁡x

Steps

Step 1 ：tan⁡2x−tan⁡x1+tan⁡2xtan⁡x=2tan⁡x1−tan2⁡x−tan⁡x1+2tan⁡x1−tan2⁡xtan⁡x

Step 2 ：2tan⁡x1−tan2⁡x−tan⁡x1+2tan⁡x1−tan2⁡xtan⁡x=2tan⁡x−tan⁡x(1−tan2⁡x)1+2tan2⁡x−tan4⁡x

Step 3 ：2tan⁡x−tan⁡x(1−tan2⁡x)1+2tan2⁡x−tan4⁡x=tan⁡x(2−1+tan2⁡x)1−tan2⁡x+2tan2⁡x

Step 4 ：tan⁡x(2−1+tan2⁡x)1−tan2⁡x+2tan2⁡x=tan⁡x(1+tan2⁡x)1+tan2⁡x

Step 5 ：tan⁡x(1+tan2⁡x)1+tan2⁡x=tan⁡x

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