Question

Solve `sinxcos``pi/6+cosxsinx``pi/6=1/sqrt2` for `0<=x,=2pi` ?

Answer 1

`pi/12; (7pi)/12`

Explanation:

Develop the left side
`LS = sin x.cos (pi/6) + cos x.sin (pi/6) = sin (x + pi/6)`
Equation to solve:
`sin (x + pi/6) = 1/sqrt2`
Trig table and unit circle give 2 solutions:
a. `x + pi/6 = pi/4`
x = `pi/4 - pi/6 = pi/12`
b. `x + pi/6 = pi - pi/4 = (3pi)/4`
`x =`(3pi)/4 - pi/6 = (7pi)/12#