Question

verify the identity. show all work. tanx+tany /cotx+cot y= tanxtany

Answer 1

this one is easy,
write tan x = 1/cot x and tan y = 1/ cot y

Answer 2

do we have to change it in terms of sin and cos ?

Answer 3

not required here, we can play with tan and cot to get the right side...

Answer 4

ohh ok cuz i started with putting everything in terms or sin and cos but i got stuck

Answer 5

so what will be your numerator ?
tan x = 1/cot x and tan y = 1/ cot y

Answer 6

(1/cotx)+(1/coty)

Answer 7

@hartnn we cannot do the opposite, for example get cotx=1/tan x ans same for the y?

Answer 8

ofcourse you can do that, bob,same thing :)
(1/cotx)+(1/coty)= ?

Answer 9

Oh okay, sorry got a little bit confused.

You would end up with (cotx+coty)/(cotx*coty)

Answer 10

i asked tammy.

Answer 11

im confused what do u do after u change it to cot

Answer 12

cross-multiply
\(\huge \frac{1}{cotx }+\frac{1}{cot y}= \frac{cot x+cot y}{cot x \: \: cot y}\)
got this ?

Answer 13

yea

Answer 14

that was your numerator, now does anything gets cancelled out ?

Answer 15

yea the numerator is cotx+coty/cotx+cot y
and the denominator is cotx+coty therefore one of them cancels from the numerator and den. and you get cotx+cot y

Answer 16

sorry u have 1 over cotxcoty which is equal to cotx+coty

Answer 17

i mean tanx +tan y

Answer 18

u have 1/ (cot x cot y )
now convert cot x = 1/tan x and cot y = 1/ tan y

Answer 19

yea i got it (:

Answer 20

good :)