Question

Help me verify this identity please?
cos(x+(pi/2))=-sin x

Answer 1

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

Answer 2

it's actually cos(x + pi/2) = -sinx

so cos(A + B) = cos(A)cos(B) - sin(A) sin(B)

Answer 3

Okay, cos(pi/2) is zero, so that disappears, and sin(pi/2) is one, so that simplifies, but how do I get rid of the cos(x) in cos(x)-sin(x)?

Answer 4

Can you explain that part to me @RadEn ?

Answer 5

what do you means, cos(x) in cos(x)-sin(x) ?

Answer 6

Oh, sorry. Not very clear. When you turn cos(x + pi/2) = -sinx into cos(x)cos(pi/2) - sin(x) sin(pi/2), the cos(pi/2) and sin(pi/2) go away, and you're left with cos(x)-sin(x). I just need -sin(x), but I don't know how to get rid of the cos(x)...

Answer 7

like as you said above, cos(pi/2) is zero, and sin(pi/2) is one.
just apply them into that formula :
cos(x + pi/2)
= cos(x)cos(pi/2) - sin(x)sin(pi/2)
= cos(x) * 0 - sin(x) * 1
= 0 - sin(x)
= -sin(x)

Answer 8

Oh, Lord. I totally forgot I was multiplying those.. Wow. Thatnks for helping me out with that brain fart. :P God bless you guys!

Answer 9

you're welcome :)