How can I prove the trig identity sinxcosxsec^2x = tanx?

[seastick]

1. How do I prove sinxcosxsec^2x=tanx

Homework Equations

sec^2x = tan^2x + 1

The Attempt at a Solution

sinxcosx(tan^2x + 1)
tan^2xsinxcosx +sinxcosx
sin^2x/cos^2x*sinxcosx + sinxcosx - is this valid?

I'm not sure what I've done is even correct - but it doesn't seem to be going anywhere helpful?

 

[The Chaz]

Rewrite secant squared as 1/cos squared. The you'll have (sincos)/(coscos). Cancel cosines and you're done. I'll edit this from my computer and add arguments later!

 

[iRaid]

secant = 1/cosine
cosecant = 1/sine
cotangent = 1/tangent

 

[The Chaz]

secant = 1/cosine
cosecant = 1/sine
cotangent = 1/tangent

SOHCAHTOA. qed

 

[seastick]

Many thanks for your help

 

[HallsofIvy]

SOHCAHTOA. qed

Wasn't that Lewis and Clark's indian guide?

 

[The Chaz]

No, this is the one that's featured on the new US coins ;)