10-1

sin(30degrees+theta)+sin(30degrees-theta)
sin30degrees*cos theta+cos30degrees*sin theta+sin30degrees*cos theta-cos30degrees*sin theta
(1/2)cos theta+(square root of 3/2)sin theta+(1/2)cos theta-square root of 3/2)sin theta
1cos theta=cos theta

To solve this problem, you have to look at the formulas and find the formula that matches with this problem.  Sin(theta+/-beta)=sin theta*cos beta+/-cos theta*sin beta is the formula you need for this problem.  Once you figure out what formula to use, you plug what you have into the formula.  Then you find the exact values of what you have.  Look on your trig chart for the exact value of sin30 and cos30.  Sin30 is 1/2 and cos30 is square root of 3/2.  Then, you can cancel the +square root of 3/2sin theta and -square root of 3/2sin theta out.  Now all you have left is (1/2)cos theta+(1/2)cos theta.  1/2+1/2 is 1 and you keep the cos theta.  So 1cos theta equals cos theta.