Question

How do I prove this??????
1 + tanx (tan(x/2)) = secx

Answer 1

\[1+\frac{\sin x}{\cos x}(\frac{1-\cos x}{\sin x})=1+\frac{1-\cos x}{\cos x}=\]

Answer 2

\[1+\frac{1}{\cos x}-\frac{\cos x}{\cos x}=1+\sec x-1=\sec x\]

Answer 3

I'm not understanding what you just did
Could you explain?

Answer 4

I replaced tanx with sin/cos
I replaces tan(x/2) with (1-cosx)/sinx
I cancelled sinx from numerator and denominator
I split the fraction into two fractions
I replaced 1/cosx with secs.
I replaced cosx/cosx with 1
I subtracted 1-1

Answer 5

Awesome, would this be the standard method for proving problems or is it just for this problem?

Answer 6

It would be standard form for proving identities.

Answer 7

So just to be clear I can use the steps you just provided for proving all identities?

Answer 8

No. Only the ideas transfers to another problem. The ideas of making the proper substitutions and simplifying and of working on one side only. Every problem is unique.

Answer 9

Ok