Question

Verify the identity.

cotx minus pi divided by two. = -tan x

Answer 1

Use sin(x-pi/2)=cos(x)
and consequently
cos(x-pi/2)=sin(x-pi)=-sin(x)

Answer 2

wouldnt you use the sum and difference formula of tan to solve?

Answer 3

tan(x ± y) - (tan x plus or minus tan y) over 1 minus or plus tan x tan y)

Answer 4

Yes, that would be shorter!

Answer 5

would you just use the inverse of the sum and difference formula of tan to find it for cot and then simplify?

Answer 6

mathmate

Answer 7

@mathmate

Answer 8

@ParthKohli could you provide some assistance with this problem if you could

Answer 9

or if any of the online mathematicians could @jim_thompson5910 @hartnn @jdoe0001 @zepdrix

Answer 10

i would still suggest using

"Use sin(x-pi/2)=cos(x)
and consequently
cos(x-pi/2)=sin(x-pi)=-sin(x)"

and before that, use

cot = cos/sin

Answer 11

Use of the tan formula involves taking limits (because of tan(-pi/2), which make it a little more messy.

Something along the lines of:

tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b)
=(tan(a)/tan(b)+1)/(1/tan(b)-tan(a))

or
cot(a+b)=( 1/tan(b) - tan(a)) / ( tan(a)/tan(b) +1)
Set a=x and let b-> -pi/2
cot(x-pi/2) = (0-tan(x)) / ( 0+1)
=-tan(x)

Answer 12

i would like to thank both @hartnn and @mathmate for your help and i appreciate you for taking the time to provide assistance as it is extremely helpful to all of us that you aid.

Answer 13

welcome ^_^
happy to help :)

Answer 14

Glad to be of help! You're welcome!
Also thank you for taking the time to show your appreciation.

Answer 15

lol, thank you for saying thank you :P