Question

write the trig expression in terms of sine and cosine then simplify.

cos t tan t


cos t csc t

Answer 1

\[\tan t = \frac{\sin t}{\cos t} \\
\cot t = \frac{\cos t}{\sin t} \\
\sec t = \frac{1}{\cos t} \\
\csc t = \frac{1}{\sin t} \]
Just some definitions that would help. You basically just substitute the definition with sines/cosines and simplify from there.

Answer 2

Ok so what's the answer?

Answer 3

Try doing the problem as I said and find out. ;)

Answer 4

im so lost

Answer 5

We have: \(\cos t \tan t\)
By definition, \(\large{ \tan t = \frac{\sin t}{\cos t} } \)
So, we can substitute the definition of \(\tan t\) for it in the expression:
\[ \cos t \times \frac{\sin t}{\cos t} = \frac{\sin t \cos t}{\cos t}\]

There, you can simplify further because the \(\cos t\)'s will have both one in the numerator and denominator.