Answer : A and D
Given,
cos(x) cos([tex] \frac{\pi}{7} [/tex]) + sin(x) sin([tex] \frac{\pi}{7} [/tex]) = -[tex] \frac{\sqrt{2}}{2} [/tex]
we know the identity
cos(x)cos(y) + sin(x) sin(y) = cos(x - y)
cos(x) cos([tex] \frac{\pi}{7} [/tex]) + sin(x) sin([tex] \frac{\pi}{7} [/tex]) = -[tex] \frac{\sqrt{2}}{2} [/tex]
cos (x - [tex] \frac{\pi}{7} [/tex]) = -[tex] \frac{\sqrt{2}}{2} [/tex]
(x - [tex] \frac{\pi}{7} [/tex]) = [tex] cos^{-1} ( -\frac{\sqrt{2}}{2} ) [/tex]
We know that ,
[tex] cos^{-1} ( -\frac{\sqrt{2}}{2} ) [/tex] is [tex] \frac{3\pi}{4} and \frac{5\pi}{4} [/tex]
x - [tex] \frac{\pi}{7} [/tex] = [tex] \frac{3\pi}{4} [/tex] + [tex] 2n\pi [/tex]
So x = [tex] \frac{3\pi}{4} [/tex] + [tex] \frac{\pi}{7} [/tex] + [tex] 2n\pi [/tex]
x - [tex] \frac{\pi}{7} [/tex] = [tex] \frac{5\pi}{4} [/tex] + [tex] 2n\pi [/tex]
So x = [tex] \frac{5\pi}{4} [/tex] + [tex] \frac{\pi}{7} [/tex] + [tex] 2n\pi [/tex]
So answer is option A and D
