Differentiating Trig Identities: Example

[cscott]

How can I use trig identities to let me differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x?

 

[Jameson]

Well, there's an identity for \sin{(\alpha+\beta)} but why would you want to use it? Those can be differentiated easily... I'm missing something.

 

[TD]

Well, \sin \left ( x + \frac{\pi}{2} \right) = \cos x if that helps

I don't see why you'd want to change the second one though, taking the derivative is lineair so \left( {3\sin x - 2\cos x} \right)^\prime = 3\left( {\sin x} \right)^\prime - 2\left( {\cos x} \right)^\prime

 

[cscott]

Damn, I guess I wasn't looking at them right. Thanks.

 

[Hurkyl]

You don't need trig identities to differentiate those...