Find approximate solution for the equation in the interval -π
tan x= 2 csc x

Option a.

-1.144 , 1.144

Step-by-step explanation:

Since we are dealing with trascendental equations, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.

Please, see attached image

We graph both equations and find the intersection between them in the interval from -pi to pi

This will give the solution to the equation

tan(x) = 2* csc(x)

The answer is

x = -1.144

x =  1.144

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

yes

step-by-step explanation:

yes