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mybarr01 · Feb 5, 2009, 11:40 AM

I need help solving equations where I need to verify the identity using the trigonometric identities.

1.) tan x cos x= sin x
2.) csc x/ sin x(1- cos^2)=1
3.) sec x- cos x= tan x sin x

galactus · Feb 5, 2009, 12:05 PM

[QUOTE=mybarr01;1529948]i need help solving equations where i need to verify the identity using the trigonometric identities.

I will do one of them so you can see what the idea is. You must use your identities.

3.)Show $sec(x)- cos(x)= tan(x) sin(x)$

Doesn't $sec(x)=\frac{1}{cos(x)} \;\ \text{and} \;\ 1-cos^{2}(x)=sin^{2}(x)$ ?

These are some of the most used of the identities. Remember and make use of them.

Therefore, $sec(x)-cos(x)=\frac{1}{cos(x)}-cos(x)=\frac{1-cos^{2}(x)}{cos(x)}$

$=\frac{sin^{2}(x)}{cos(x)}=\frac{sin(x)}{cos(x)} \cdot sin(x)=tan(x) \cdot cos(x)$

Now, you try the other two and let me see how you're progressing.