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# P2 pure maths trig continued watch

1. Tan 2x = tan x
between 0 and two pi

pls show full steps I ended up with

(tan x)(sec x) = 0

I can get solution for tan, but I don't know how to work out for sec X ?? ideas

2. tan2x = 2tanx/(1-tan²x)

=> 2tanx/(1-tan²x) = tanx
2tanx = tanx - tan³x
tan³x + tanx = 0
tanx(tan²x+1) = 0
tanx.sec²x = 0

sec²x = 1/cos²x, so sec²x = 0 has no solutions.

tanx = 0
x = 0 , pi , 2pi (or 3.14 and 6.28, if you wanna decimalise it)

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