Question

Find all solutions of the equation on the interval [0,2pi):

Tan^2x=1-secx

Answer 1

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)=1-sec(x)

and click option =

After few secons you will see result.
Then clic option Show steps

Answer 2

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

Answer 3

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

Answer 4

Thank you!

Answer 5

find all solutions to the equation 2x^3+12x^2+50x=0