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

Question

trigonometry problem, find the trig identity

Answer 1

Given trig identity is sinxcos(pi/6)+sin(pi/6)cosx = 1/√2

Remember the formula

sin(A+B) = sinAcosB+cosAsinB

Sinxcos(pi/6)+cosxsin(pi/6) = 1/√2

sin(x+pi/6) = 1/√2

sin(x+pi/6) = sin(pi/4)

x+pi/6 = pi/4

x = pi/4-pi/6

x = pi/12

Weknow that pi/12 = 15degrees

Check

pi/6 = 30,pi/12 = 15

sin(15+30) = sin45 = 1/√2