Question

Which of the following are solutions to the equation
sinx cos(π/7) - sin (π/7) cos x = √2/2

Answer 1

A. π/4 + π/7 + 2nπ
B. 5π/4 + π/7 + 2nπ

Answer 2

C. 7π/4 + π/7 + 2nπ
D. 3π/4 + π/7 + 2nπ

Answer 3

Well, this is actually an identity, it just might be hard to recognize. This is a difference of sines formula. The original of this is sin(x-pi/7). So basically, we need to see when sin(x-pi/7) = sqrt(2)/2. So to start, what are the values of sin that will get you sqrt(2)/2?

Answer 4

I was thinking A and B because I would end up with a negative answer for C and D.

I'm not looking for the answer. I want to know how to get there. The steps!

Answer 5

sin(a - b) = sin a cos b - sin b cos a

LHS is
sin(x - π/7) = √2/2

sin is √2/2 at π/4 and 3π/4
therefore
x - π/7 = π/4, x = 11π/28 + 2kπ
x - π/7 = 3π/4, x = 25π/28 + 2kπ

Answer 6

Right, pretty much. I just wanted to check both answers since both A and D seem to check out O.o

Answer 7

Yeah, it really looks as if both A and D are correct.