# Trig

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

Tan^2x=1-secx

1. 👍 0
2. 👎 0
3. 👁 254
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

1. 👍 0
2. 👎 0
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

1. 👍 0
2. 👎 0
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

1. 👍 0
2. 👎 0
4. Thank you!

1. 👍 0
2. 👎 0
5. find all solutions to the equation 2x^3+12x^2+50x=0

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) Find the solutions in the interval:

asked by Janet on April 27, 2019
2. ### Trigonometry

Find all solutions of the equation in the interval [0,2pi). sec(theta)+2=0 Write your answer in radians in terms of pi

asked by Pascal on March 25, 2014
3. ### Trig

Find all solutions of the equation in the interval [0,2pi). 2sin theta+1=0. Write answer in radians in terms of pi.

asked by James on August 19, 2015
4. ### Algebra 2

Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

1. ### Math

1. On the interval [0, 2pi] what are the solutions to the equation sin3xcos2x = -cos3xsin2x + 1? pi/10 and pi/2? 2. What is the value of tan75degrees? √(3) + 1)/(1 - √(3))? 3. Value of cos(130degrees)cos(130degrees) +

asked by mysterychicken on June 3, 2013
2. ### Math

how many solutions does the equation sin(5x)=1/2 have on the interval [0,2pi]?

asked by Lizzie on November 22, 2013
3. ### Trig

Find all solutions of the equation in the interval [0,2pi). sqrt(3)cottheta-1= 0 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

asked by Rachal on May 15, 2011
4. ### solving trig. equations

tan(3x) + 1 = sec(3x) Thanks, pretend 3x equals x so tanx + 1 = secx we know the law that 1 + tanx = secx so tanx + 1 becomes secx and... secx = secx sec(3x) = sec(3x) [just put 3x back in for x- you don't really have to change 3x

asked by Jen on April 12, 2007
1. ### Math

Find all the solutions of the equation in the interval {o,2pi) sec^2x+tanx=1

asked by Tonya on February 8, 2015
2. ### Precalc

Find the exact solutions to each equation for the interval [0,360) 2cosx-secx = 1

asked by Sean on December 6, 2007
3. ### pre calc

Find all solutions of the equation 3sin^2 x -7sin x +2 = 0 in the interval [0,2pi). The answer is x_1= ?? and x_2= ?? with x_1

asked by james on April 14, 2013
4. ### math

Find all solutions to the equation tan(t)=1/tan (t) in the interval 0

asked by alicia otto on March 26, 2016