Can someone explain trig identities to me? Thanks! ;)

Question

anonymous · Answer

The main one to remember is the Pythagorean identity:
$$\sin^2t+\cos^2t=1$$
Here's a simple proof. Take some arbitrary right triangle:|dw:1370917206600:dw|
Next, see what happens when you divide both sides of the equation by $\sin^2t$:
$$\frac{\sin^2t}{\sin^2t}+\frac{\cos^2t}{\sin^2t}=\frac{1}{\sin^2t}\
1+\cot^2t=\csc^2t$$
Likewise, see what happens when you divide both sides of the equation by $\cos^2t$:
$$\frac{\sin^2t}{\cos^2t}+\frac{\cos^2t}{\cos^2t}=\frac{1}{\cos^2t}\
\tan^2t+1=\sec^2t$$
Of course, there are others, but I'd say this is the single most important trig identity to know. Your question's a bit too general. Are there any specific identities you're having trouble with?