Question

Verify the identity.

cotx - pi / two. = -tan x

Answer 1

( )

Answer 2

can you take out the negative sign first and then use the identity

Answer 3

Im not sure how to do this at all

Answer 4

well are you familiar with Cofunctions Identities ?

Answer 5

a little bit

Answer 6

remember cot(-x)=cot x
not what would you get when you take out negative sign from (x-pi/2) ?

Answer 7

some things

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

cot(-x) = -cot x
tan(-x) = -tan(x)
.
.

Answer 8

pi/2

Answer 9

\[\rm (x- \frac{\pi}{2})\] in other words
-1 is a common factor so when we take out common factor we should divide both terms by the common factor

so \[\cot(\frac{ x }{ -1} -\frac{ \frac{ \pi }{ 2 } }{ -1 })\]
so when you divide x by negative one what would you get ?
(pi/2) divide by -1 =?

Answer 10

- pi over 2

Answer 11

ugh nvm sorry it's (-pi/2) divide by -1 .

Answer 12

oh pi/2

Answer 13

?

Answer 14

..correct negative divide by negative = positive
and negative divide by positive = negative
xo x/-1 = -x
so when you take out -1 from x u will get -x
\[\rm \cot(-[\frac{ \pi }{ 2 }-x])\]and keep the common factor outside the bracket which is negative one
now use the fact cot(-x)=-cot(x) (odd function ) and then use the identity

Answer 15

http://www.analyzemath.com/trigonometry/trigonometric_formulas.html here are trig identities u should copy these down n ur notebook :=))

Answer 16

What would i write as my final answer?

Answer 17

yeah, knowing the symmetries and coordinate sign changes on the circle helps alot to remember some things, symmetries

Answer 18

`verify` the identity you need to prove that L.H.S is equal to R.H.S

Answer 19

how?

Answer 20

what we just did ?
we were working on left side to prove that it's equal to -tan(x)

Answer 21

look at the identity ^above (7th comment ) cot(pi/2-x)=tan(x) use that

Answer 22

let me ask u something
if cot is an odd function then cot(-x)= -cot(x)
here is an example \[\cot (\color{ReD}{-}4\pi) = -\cot (4\pi) \]
so how would you write \[\cot (\color{ReD}{-}[\frac{\pi}{2}-x]) = ?\]