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tan x + (tan x)(sec 2x) = tan 2x work dependently on the left side

tan x + (tan x)(sec 2x); factor out tan x

= tan x(1 + sec 2x); sec 2x = 1/cos 2x

= tan x(1 + 1/cos 2x); LCD = cos 2x

= tan x[cos 2x + 1)/cos 2x]; tan x = sin x/cos x and cos 2x = 1 - 2 sin2 x

= (sin x/cos x)[(1 - 2sin2 x + 1)/cos 2x]

= (sin x/cos x)[2(1 - sin2 x)/cos 2x]; 1 - sin2 x = cos2 x

= (sin x/cos x)[2cos2 x)/cos 2x]; simplify cos x

= (2sin x cos x)/cos 2x; 2 sinx cos x = sin 2x

= sin 2x/cos 2x

= tan 2x

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Q: How do you prove tan x plus tan x sec 2x equals tan 2x?
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