Question

For what values of t, is tan t=cot t ?

A. t= pi/4 + pi/2 x k where k is an integer

B. no matter what value of t is, tan t is always different than cot t

C. t=1

D. t= pi/4 + pi x k where k is an integer

***I don't really remember the rules.. could you please refresh me and explain? Thank youu :)

Answer 1

\(\tan t = \dfrac{\sin t}{\cos t} \)


\( \cot t = \dfrac{\cos t}{\sin t} \)

Make these substitutions in your equation.
Then cross multiply.
What do you get?

Answer 2

umm i'm not quite sure what you mean :(

Answer 3

which equation am i substituting it in? :/

Answer 4

sorry i'm a bit confused :(

Answer 5

Your eq. has tan t and cot t.
I wrote above two identities of what tan t is equal to and what cot t is equal to.
Start with your equation, tan t = cot t.
Now substitute tan t with what tan t is equal to.
Substitute what cot t with what cot t is equal to.
What do you get?

Answer 6

ohhh so i cross multiply and get sin t^2 = cos t^2 ? :/

Answer 7

\( \dfrac{\sin t}{\cos t} = \dfrac{\cos t}{\sin t} \)

\(\sin^2 t = \cos^2 t\)

Answer 8

ohhh okay what happens from here?

Answer 9

\(\sin^2 t - \cos^2 t = 0\)

\((\sin t + \cos t)(\sin t - \cos t) = 0\)

\(\sin t = - \cos t\) or \( \sin t = \cos t\)

Where do the sine and cosine functions have the same value?