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

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.


[quote]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.