Proving (sec²x-1)/sec²x = sin²x and cos²x/(1+tan²x) = cot²x

[chase222]

I need help solving these 2 proofs:

(sec^2x-1)/(sec^2x) = sin^2x
I am not sure what direction to go in. I know the top of the left side could be changed into:
tan^2x/sec^2x, but I don't know what to do after that.

The second one I need help with is:

cos^2x/(1+tan^2x) = cot^2x
I simplified it into:
cos^2x/sec^2x = cos^2x/sin^2x, but I don't know what to do after that. Can you help me get the next few steps of these problems? Thanks!

 

[Imo]

Actually, your already done...you just don't know it.

(sec^2x-1)/(sec^2x) = sin^2x
I am not sure what direction to go in. I know the top of the left side could be changed into:
tan^2x/sec^2x, but I don't know what to do after that.

remember that tanx=sinx/cosx? try that

The second one I need help with is:

cos^2x/(1+tan^2x) = cot^2x
I simplified it into:
cos^2x/sec^2x = cos^2x/sin^2x, but I don't know what to do after that. Can you help me get the next few steps of these problems? Thanks!

this one is done. again, remember that cotx=1/tanx, so what is cotx in terms of sin and cos?

 

[nomorevishnu]

chase...u seem to be a small boy just starting to learn math...am i right?

first problem...sec^2 x-1/sec^2 x=sin^2 x...
ie...tan^2 x/sec^2 x=RHS
ie...sin^2 x*cos^2 x/cos^2 x...that is equal to sin^2 x...isnt it?/
and the second problem u have given is wrong...there is some mistake in it...dont worry..trigonometry is easy...just try to create equations urselves...solve most of them using mind...then take ur pen...because u should be learning them like drinking water...so have them in ur fingertips...