Question

Please help i dont know how to do this:
Verify the identity:
cos(x+(pi/2))=-sin(x)

Answer 1

How about using the identity \(\cos(u+v) = \cos u\cos v - \sin u\sin v\) on \(\cos(x+\pi/2)\) and see what develops?

Answer 2

i replace that with the cos(x+(pi/2)

Answer 3

?

Answer 4

let u = x, v = pi/2 and expand that identity. it would replace the left hand side of your equation...

Answer 5

Your left hand side is \(\cos (x + \pi/2)\) which is the cosine of a sum. That identity I gave you expands the cosine of a sum.

Answer 6

i see so i put cos x cos pi/2 - sin x sin pi/2

Answer 7

then simplify and then ill get the same as the right side?

Answer 8

Well, try it and see!

Answer 9

A lot of these problems you do quite a bit of the learning just by going through the steps and writing them out. Looking at it and saying "oh, yeah, I see" doesn't have the same effect.

Answer 10

i see but how would i make them alike?

Answer 11

i need to subsitute cos to make sin

Answer 12

What is the value of \(\cos \pi/2\)? How about \(\sin\pi/2\)?

Answer 13

cos(pi/2)= 0

Answer 14

Yes. What about sin?

Answer 15

1

Answer 16

Okay, so what does the left half become after you substitute in those values?

Answer 17

cos(x)-sin(x)+1

Answer 18

so now we have to get rid of the cos(x) and the +1

Answer 19

No...you have\[\cos(x+\pi/2) = -\sin x\]
We substitute the angle sum identity for cosines on the left, with u = x, and v = pi/2:\[\cos x\cos \pi/2 - \sin x\sin \pi/2 = -\sin x\]\[\cos \pi/2 = 0\]\[\sin \pi/2 = 1\]Substitute those values into the equation
\[0*\cos x - 1 *\sin x = -\sin x\]\[-\sin x = -\sin x\]