Question

which of the following are solutions to the equation sinx cos(pi/7)-sin(pi/7)cosx=sqrt(2)/2
check all that apply
A. 7pi/4+pi/4+2npi
B. 5pi/4+pi/7+2npi
C. pi/4+pi/7+2npi
D. 3pi/4+pi/7+2npi

Answer 1

I can not figure this out

Answer 2

sinx cos(pi/7) - sin(pi/7) cosx = sqrt(2)/2
sin(x - pi/7) = sqrt(2)/2

x - pi/7 = pi/4 or x-pi/7 = 3pi/4

x = (11pi/28) + k(2pi)
or
x = (25pi/28) + k(2pi), where k is an integer

So actually both C and D are the the solutions

Answer 3

thats what i thought but then i doubted myself. thanks

Answer 4

your welcome!