Question

How do you verify:
1.) sinxcosx+sinx^3secx=tanx

2.) (secx+tanx)/(secx-tan)=(secx+tanx)^2

I tried starting from the left on both problems, but am stuck.

like I said before, change everything into sines and cosines.

for the first one:
LS= sinxcosx + (sin^3x)cosx
=(sinxcos^2x + sin^3x)/cosx
=
=
factor out the sinx, and look what you have left inside the bracket!
two more steps!

the second one is just as easy.

LS = (1/cosx + sinx/cosx)(1/cosx - sinx/cosx)
=
=

can you see the common factor, and the difference of squares pattern?