Prove this trigonometry identities

What are the steps to proving the following Trigonometry identity? tan 2x/tan x = 1 + sec 2x
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tan(2x)/tan(x)=[2tan(x)/(1-tan²(x))]/tan(x)=2/(1-tan²(x))=

2cos²(x)/(cos²(x)-sin²(x))=

2cos²(x)/cos(2x)=

2cos²(x)sec(2x)=(1+cos(2x))sec(2x)=

sec(2x)+1, same as 1+sec(2x), QED

 

by Top Rated User (1.1m points)

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