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# [hs calculus] Analytic Trigonometry

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i need to find the solution for the following:

22: cos2 (x(sec2 (x) -1))

23: sec4 (x) - tan4 (x)

24: cot (x sec(x))

25:(sec2 (x) -1)/sin2 (x)

26:cos2 ((pi/20) - x)/cos(x)

I am completely lost please show me how to solve these kinds of problems.

Guest May 6, 2017
#1
+93691
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Hi,

Firstly you cannot get a solution becasue there is no equal sign.

All you can do it try to simplify them :)

I am confused about what the actual questions are.

I assume there are a number of powers here.

23: sec4 (x) - tan4 (x)

I assume

$$sec^4 (x) - tan^4 (x)\\ \qquad \text{Difference of 2 squares}\\ =(sec^2 (x) + tan^2 (x))(sec^2 (x) - tan^2 (x))\\ \qquad sec^2x=\frac{1}{cos^2x}=\frac{sin^2x+cos^2x}{cos^2} =tan^2x+1 \\ =(1+tan^2(x) + tan^2 (x))(1+tan^2x- tan^2 (x))\\ =1+2tan^2(x) \\$$

Melody  May 6, 2017
#2
+93691
+1

By the way, simplifying these expressions has nothing to do with calculus.

Do you mean something different?  Maybe you want them differentiated or integrated?

I think I will let you comment before I play with any more of them.

Melody  May 6, 2017
edited by Melody  May 6, 2017