Determine the specific solutions if any to the equation on t

Determine the specific solutions (if any) to the equation on the interval [0, 2pi). Tan theta = - Squareroot 2 sin theta What is the solution in the interval 0less-thanorequalto theta less-thanorequalto 2 pi ? Select the correct choice and fill in any answer boxes in your choice below. Theta = squarebox (Use a comma to separate answers as needed. Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.) There is no solution.

Solution

tan theta=-sqrt2 sin theta

tan theta + sqrt2 sin theta=0

tan theta=sin theta/cos theta

sin theta/cos theta   + sqrt2 sin theta=0

sin theta(1/cos theta   + sqrt2)=0

sin theta=0   and 1/cos theta=-sqrt2

sin theta=0 and cos theta=-1/sqrt2

Taking inverse function on both sides

theta= sin^-10         and theta= cos^-1(-1/sqrt2)

theta=0,pi and   theta= 3pi/4,5pi/4

theta=0,pi,3pi/4,5pi/4