Question

find all solutions of the equation on the interval [0,2pie)
cos(x+pie/4)-cos(x-pie/4)=1

Answer 1

you have to use the sum and differnce formula

Answer 2

thats right...\[\cos p-\cos q=-2\sin(\frac{p+q}{2})\sin(\frac{p-q}{2})\]

Answer 3

wrong

Answer 4

it's right..

Answer 5

then cos(x+pie/4)-cos(x-pie/4)= -2sin(x)sin(pie/4) = 1

then sin(x)sin(pie/4) = -1/2

Answer 6

\[\cos (x+a)-\cos (x-a)=-2\sin(\frac{x+a+x-a}{2})\sin(\frac{x+a-x+a}{2})\]\[\cos (x+a)-\cos (x-a)=-2\sin x\sin(a)\]

Answer 7

can you find answer??

Answer 8

your a is pi/4

Answer 9

finally sinx = -(1/root(2))

Answer 10

so x is (5/4)pi and (7/4)pi

Answer 11

wow how did you do that

Answer 12

final eq sinx = -(1/root(2)) means that x is over the angle pie