Question

Proving trig functions with substitution

I understand that I need to substitute in trig identities, but I don't understand the steps to do it.
Questions:
https://gyazo.com/940b577311db9eba1a525de731d0b661

Trig identities to use: https://gyazo.com/95a7016e9594eddf96e7927561f2b6d0

Answer 1

We want to show one side is the other side.
Let's look at the first one and try to show the left hand side is the right hand side

Answer 2

\[\cot(x) \sec^4(x)\]
try using a Pythagorean identity and then expanding

Answer 3

In doing this would you be, for example, dividing it by a term? Or is this the result of it?

Answer 4

Not sure what you mean

you know that sec^4(x) is the same as (sec^2(x))^2
so you can use a Pythagorean identity to write this part in terms of tan(x)

Answer 5

So because you have sec^2 in the equation, you would be able to "pull it out" (don't know how to really explain it" and use the identity sec^2u = 1 + tan^2u?

Answer 6

yes replace sec^2(x) with 1+tan^2(x)

Answer 7

you will have a binomial to expand
and then multiply that product by the cot(x) factor you have

Answer 8

\[\cot(x) (\sec^2(x))^2 \\ \cot(x)(\sec^2(x))^2 \\ \text{ use } \sec^2(x)=\tan^2(x)+1\]

Answer 9

Ok. That was confusing me. I was trying to figure out where that came from.

Answer 10

can you show me how far you have gotten