Question

prove the conjunction identity sin(pi/2-x)=sin (pi/2+x)

Answer 1

guess you are supposed to use the addition angle formula on the right and the subtraction angle formula on the left and see that you get the same thing

Answer 2

which ought to be \(\cos(x)\)

Answer 3

not sure that helped, if you are still confused let me know

Answer 4

well my teacher told us not to do it that way so I do not know what other way I can prove that the two are equal

Answer 5

not to use the fact they they were both cosine?

Answer 6

yes. He wanted us to prove that they were equal by changing on side of the equation to match the other side

Answer 7

i can show you why they are obviously the same

Answer 8

another thing you could try (requires knowing that \(\sin(x)=-\sin(x+\pi)\) is to right the left hand side as
\[\sin(\frac{\pi}{2}-x)=-\sin(x-\frac{\pi}{2})\]

Answer 9

that because sine is odd

Answer 10

lol *write the left hand side ..."

Answer 11

then add \(\pi\) to the input, change the sign again and get \(\sin(x+\frac{\pi}{2})\)

Answer 12

ok that helps thank you