verifying 2 trig identities

[helpmewtrig]

i have no idea how to verify these two trig identities

1. 2sec^2 x-2sec^2 x*sin^2 x-sin^2 x-cos^2 x=1

2. cos^3 x-sin^3 x/cos x-sin x = 1+sin x*cos x

if you could help with this i would be very grateful

THANK YOU

 

[Deleted member 4993]

i have no idea how to verify these two trig identities

1. 2sec^2 x-2sec^2 x*sin^2 x-sin^2 x-cos^2 x=1

2. cos^3 x-sin^3 x/cos x-sin x = 1+sin x*cos x

if you could help with this i would be very grateful

THANK YOU

1) Hint - factor out \(\displaystyle \sec^2\theta\) and use

\(\displaystyle \sin^2\theta \, + \, \cos^2\theta \, = \, 1\)

2) Hint:
\(\displaystyle a^3 \, - \, b^3 \, = \, (a-b)\cdot(a^2 \, + \, ab \, + \, b^2)\)

 

[helpmewtrig]

thank you so much i really do appreciate your help