Question

Solve: tanx.tan4x=1
Find general solution

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Answer 1

Answer:

Dear Student,

tan x tan 4x=1tan 4x=1tan xtan 4x=cot x=tan(π2−x)tan 4x−tan(π2−x)=0sin 4xcos 4x−sin(π2−x)cos(π2−x)=0sin 4x cos(π2−x)−sin(π2−x) cos 4xcos 4x cos(π2−x)=0sin 4x cos(π2−x)−sin(π2−x) cos 4x=0sin(4x−(π2−x))=0sin(4x−π2+x)=0sin(5x−π2)=05x−π2=nπ, n∈Z5x=nπ+π2, n∈Zx=nπ5+π10, n∈Z