Trig
posted by Lsat on .
Find all solutions of the equation on the interval [0,2pi):
Tan^2x=1secx

In google type:
wolfram alpha
When you see lis of results click on:
Wolfram Alpha:Computational Knowledge Engine
When page be open in rectangle type:
solve tan^2(x)=1sec(x)
and click option =
After few secons you will see result.
Then clic option Show steps 
Remark:
When you see step
Simplify trigonometric functions:
If we know that:
tan^2(x)=sec^2(x)1
tan^2(x)+sec^2(x)1=0 becomes:
sec^2(x)1+sec(x)1=0 
sec^2 x  1= 1  secx
sec^2 x + sec x  2 = 0
(secx + 2)(secx 1) = 0
secx = 2 or secx = 1
cosx = 1/2 or cosx = 1
x = 120° or x = 240° or x = 0 or x = 360°
x = 0, 2π/3 , 4π/3, 2π 
Thank you!

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