Question

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

Answer 1

try writing that left side in terms of cosine and sine.... what u got?

Answer 2

after you do that, use the sum and difference rule for sine and cosine.... you should be able to simplify easily from there....

Answer 3

hold on

Answer 4

\(\cot(x) = \frac{ \cos(x) }{ \sin(x) }\) and \(\tan(x) = \frac{ \sin(x) }{ \cos(x) }\)

Answer 5

ok can u show me how to get that

Answer 6

as @abb0t stated, cotx = cosx/sinx.... so
\(\large cot(\theta - \pi/2)=\frac{cos(\theta-\pi/2)}{sin(\theta-\pi/2)}\)

Answer 7

now, use the difference rules for sine and cosine...

Answer 8

here.... check out page 2: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 9

ok its sin(x)cos(pi/2) - cos(x)sin(pi/2)

Answer 10

yes... that's for the denominator.... how 'bout the numerator?

Answer 11

hold on

Answer 12

cos(x)cos(pi/2) - sin(x)sin(pi/2)

Answer 13

very nice....
now,
cos(pi/2) = ???
sin(pi/2) = ???

Answer 14

hold on

Answer 15

oh wait....
cos(x - pi/2) = cosx cos(pi/2) + sinx sin(pi/2)
this is correct.... make sure you make the change....

Answer 16

ok i have to change the - to a +

Answer 17

thank you

Answer 18

hang on.... afk...

Answer 19

huh

Answer 20

afk: away from keyboard....
but i'm back now...

Answer 21

lol ok

Answer 22

i have a another problem i need help with