Question

cot (x-(pi/2))= -tan x

Verify the identity.

Answer 1

@nelsonjedi

Answer 2

I suppose you can write it as cosine / sine, expand using the relevant identities and simplify.

Answer 3

umm...

Answer 4

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

Answer 5

http://learn.flvs.net/webdav/educator_precalc_v12/module05/05_02_02b_b.htm

Answer 6

thats is what i have for these problems

Answer 7

That link won't work for people who don't have an account there.

Answer 8

Reciprocal Identities
sin u equals 1 over csc u cos u equals 1 over sec u tan u equals 1 over cot u
csc u equals 1 over sin u sec u equals 1 over cos u cot u equals 1 over tan u

Quotient Identities
tan u equals sin u over cos u cotangent u equals cosine u over sine u

Pythagorean Identities
sin2u + cos2u = 1 1 + tan2u = sec2u 1 + cot2u = csc2u

Cofunction Identities
sin (pi over 2) equals cos u cos (pi over 2 minus u) equals sin u
tan (pi over 2 minu u) equals cot u
cot (pi over 2 minus u) equals tan u
sec (pi over 2 minus u) equals csc u
csc (pi over 2 minus u) equals sec u

Even/Odd Identities
sin(-u) = -sinu sec(-u) = secu tan(-u) = -tanu
csc(-u) = -cscu cos(-u) = cosu cot(-u) = -cotu

Answer 9

@aum

Answer 10

but it has to equal -tanx @zzr0ck3r

Answer 11

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

Answer 12

fixed

Answer 13

Okay, they don't want you to PROVE the identity but just verify it using the identities provided in the list above.
One of the Cofunction identity states: cot (pi over 2 minus u) equals tan u
That is, cot(pi/2 - u) = tan(u) or cot(pi/2 - x) = tan(x)
Here, on the LHS. you have cot (x-(pi/2)) = cot ( - (pi/2-x) ) = -cot(pi/2 -x ) = -tan(x)

Answer 14

@ninjasandtigers do you understand?

Answer 15

yeah so we are basically just flipping the equation around a bit? @aum @zzr0ck3r

Answer 16

its just the fact that \(\cos(x-\frac{pi}{2})=\sin(x)\) and \(\sin(x-\frac{\pi}{2})=-\cos(x)\)

Answer 17

ok