Answer:
Step-by-step explanation:
Replace tan^2(x) with sin^2 (x ) / cos^2(x)
2 sec(x) sin^3(x) = cos(x) * sin^2(x) / cos^2(x) Cancel cos(x) with cos^2(x)
2 sec(x) sin^3(x) = sin^2(x) / cos(x) Multiply by cos(x) both sides
2 sec(x)*cos(x)*sin^3(x) = sin^2(x) Divide sin^2(x) both sides
Note sec(x) and cos(x) will cancel when multiplied. giving you one
2 sin^3(x) / sin^2(x) = sin^2(x) / sin^2(x) Do the division
2 sin(x) = 1 Divide by 2
sin(x) = 1/2
x = sin-1(1/2)
x = 30 degrees or 150 degrees.
So the answers are pi/6 and 5/6 pi
