Hi,

Im having a lot of trouble solving the following trig identities:

a) sec² x-2 sec x cos x + cos² = tan² x - sin² x

b) $\displaystyle tan x + 1/ tanx = 1/sin x cos x$

My working:

For a):

Trigonometric identity: secx cosx=1

Therefore:

sec²x-2 sec x cos x + cos²

=sec²x + cos²-2

Identity: sec²x = 1/cos²x

Use the Identity:

sec²x + cos²- 2

1/cos^2x +cos²x-2

Now I am very confused, really unsure on how to prove this identity. I would greatly appreciate any helpful tips.

For b)

tanx+1/tanx =1/(sinx cosx )

L.H.S:

Tanx+1/tanx

Identity: 1/tanx = cotx :

=tanx+cotx

Now im completely lost, the R.H.S side is turning out to be "csc x sec x" .

I would greatly appreciate any helpful tips, since I'm very confused here.

Thanks