Question

verify the identity. cot(x-pi/2) = -tan x

Answer 1

HI!!

Answer 2

hi!

Answer 3

what does "verify" mean in this instance? my guess is it means use the subtraction angle formula for cotangent but i could be wrong

Answer 4

im not sure

Answer 5

i don't know it, so i just looked it up
it is
\[\cot(A-B)=\frac{\cot(A)\cot(B)+1}{\cot(B)-\cot(A)}\] sort of annoying

Answer 6

actually now it is easy, since
\[\cot(\frac{\pi}{2})=0\]

Answer 7

\[\cot(A-B)=\frac{\cot(A)\cot(B)+1}{\cot(B)-\cot(A)}\]
\[\cot(x-\frac{\pi}{2})=\frac{\cot(x)\cot(\frac{\pi}{2})+1}{\cot(\frac{\pi}{2})-\cot(x)}\]

Answer 8

you get
\[-\frac{1}{\cot(x)}\] right away

Answer 9

oh ok thanks so much :)

Answer 10

actually I think I'm supposed to show how cot (x-pi/2)= -tan x

Answer 11

Keep in mind that cot and tan are inverse functions, so:

-1/cotx = -tanx