solve sinxcos(π/6) + sin(π/6)cosx= 1/√2

Question

trigonometry problem, frind the trig identity

Answer 1

Use your trig identity 

 

here aplha = pi/6

beta =x

sin( x + pi/6) = 1/roo(2)

sin(x + pi/6) = root(2)/2

(x+ pi/6) = pi/4     and (x+ pi/6) = 3pi/4

x = pi/4 - pi/6      and   x = 3pi/4 - pi/6

x = 3pi/12 - 2 pi/12     x  = 9 pi/12 - 2pi/12

x = pi/12                      x = 7pi/12