Question

If cos x cos (pi/7) + sin x sin (pi/7) =-√2/2, then x can equal:
more than one answer:

a. 3pi/4+pi/7+2 n pi
b. 7 pi/4 + pi/7 +2 n pi
c. pi/4 + pi/7 +2n pi
d. 5pi/4 + pi/7 +2 n pi

Answer 1

\[\cos a \cos b- \sin a \sin b=\cos (a+b)\]
use this.
now solve.

Answer 2

can you help more please

Answer 3

\[\cos x \cos \pi/7 + sinx \sin \pi/7= \cos(x-\pi/7)= -\sqrt{2}/2=-1/\sqrt{2}\]
\[\cos \theta=-1/\sqrt{2}.. then \theta = 3\pi/4 + 2n \pi =(x-\pi/7)\]
now try to solve it.

Answer 4

answer is a.