1. something's not working

I have three problems, and none of them seem to work. they give us a hint to use trig identities.

48) dy/dx = sec^4 (x)

50) dy/dx = 4 cos^2 (x)

52) dy/dx = (cos^4 (x) - sin^4 (x))

I have no idea how to do any of these. I spent the last 50 minutes trying

2. Originally Posted by jahichuanna
I have three problems, and none of them seem to work. they give us a hint to use trig identities.

48) dy/dx = sec^4 (x)

50) dy/dx = 4 cos^2 (x)

52) dy/dx = (cos^4 (x) - sin^4 (x))

I have no idea how to do any of these. I spent the last 50 minutes trying
48) $\displaystyle \int \sec^4 x \,dx = \int \sec^2x \sec^2x \, dx$ let $\displaystyle u = \tan x$
50) $\displaystyle \cos^2x = \frac{1 + \cos 2x}{2}$

52) factor
$\displaystyle \cos^4 x - \sin^4 x = \left( \cos^2x - \sin^2x\right) \left( \cos^2x + \sin^2x\right) = \cos 2x$

3. $\displaystyle \sec^4{x} = \sec^2{x} \cdot \sec^2{x} = (1 + \tan^2{x})\sec^2{x}$

see u and du ?

$\displaystyle 4\cos^2{x} = 4\left(\frac{1+\cos(2x)}{2}\right) = 2 + 2\cos(2x)$

$\displaystyle \cos^4{x} - \sin^4{x} = (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x} = \cos(2x)$

4. $\displaystyle \cos^4{x} - \sin^4{x} = (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x} = \cos(2x)$

I don't see how you got that math.....

$\displaystyle (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x}$

5. Originally Posted by jahichuanna
$\displaystyle \cos^4{x} - \sin^4{x} = (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x} = \cos(2x)$

I don't see how you got that math.....

$\displaystyle (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x}$[/quote]

which part do you not "see"?

6. Originally Posted by skeeter
I don't see how you got that math.....

$\displaystyle (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^2{x} - \sin^2{x}$

wouldnt that work out to be

$\displaystyle (\cos^2{x} + \sin^2{x})(\cos^2{x} - \sin^2{x}) = \cos^4{x} - \sin^4{x}$?

7. Gotta remember that Cos2(x)+sin(2)x = 1

8. Originally Posted by Slipery
Gotta remember that Cos2(x)+sin(2)x = 1
oh yeah.......ur right. i do need to study these.