How do you solve sinx cos (pi/6) + sin (pi/6) cos x= 1/sqrt2?

1 Answer
Nghi N.
Apr 12, 2016

(pi)/12 and (7pi)/12

Explanation:

Use the trig identity:
sin a.cos b + sin b.cos a = sin (a + b)
sin x.cos (pi/6) + sin (pi/6).cos x = sin (x + pi/6).
The equation transforms to:
sin (x + pi/6) = 1/sqrt2 = sin (pi/4).
The trig unit circle gives another arc (3pi)/4 that has the same sin value (1/sqrt2).
a. x + pi/6 = pi/4 --> x = pi/4 - pi/6 = pi/12
b. x + pi/6 = (3pi)/4 ---> x = (3pi)/4 - pi/6 = (7pi)/12
Answer for (0, 2pi):
pi/12 and (7pi)/12

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