Find all solutions to the equation sin pi6 x sin pi6 x 1

Find all solutions to the equation. sin (pi/6 + x) + sin (pi/6 - x) = -1 Write your answer in radians in terms of pi, and use the or button as necessar Example: x = pi/5 +2k pi, k Epsilon Z or x = pi/7 + k pi, k epsilon Z

Solution

sin( pi/6 +x) +sin( pi/6 -x)= -1

Use the formula for sin(a+b) and sin( a-b)

sinpi/6cosx +cospi/6sinx + sinpi/6cosx -sinxcospi/6 = -1

2sinpi/6cosx =-1

2(1/2)cosx =-1

cosx =-1

x= cos^-1(-1) = pi

x= pi +2k*pi