Trigonometric Identities

[NaN-Gram]

Hello again, I wanted to make a separate thread for my next question, seeing as it covers a different topic.
I have my work available, so I can show my steps.
If there's any problems with the work I've shown, I'm open to suggestions as to how to proceed.

 

[Deleted member 4993]

Hello again, I wanted to make a separate thread for my next question, seeing as it covers a different topic.
I have my work available, so I can show my steps.
If there's any problems with the work I've shown, I'm open to suggestions as to how to proceed.
View attachment 17250

The first line is incorrect. It should use : sec⁴(x) = sec²(x) * sec²(x) = sec²(x) * [1 + tan²(x)]

 

[Steven G]

I just have to give you this one as you are not seeing the value of my hint.

Break off a sec(x) from sec^4(x).

So now we have \(\displaystyle \int (sec^4(x)tan(x)dx = \int sec^3(x)(sec(x)tan(x)dx)\)

This is in the form of \(\displaystyle \int u^3du\) where u = sec(x)