How do you verify the identity #2-sec^2z=1-tan^2z#?

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Answer 1 · 2017-01-07T20:45:31

Consider the pythagorean identity #tan^2theta + 1 = sec^2theta#.

Then #tan^2theta = sec^2theta - 1#. Rewrite the starting identity in terms of secant.

#2 - sec^2z = 1 - (sec^2z - 1)#

#2 - sec^2z = 1 - sec^2z + 1#

#2 - sec^2z = 2 - sec^2z#

#LHS = RHS#

Identity proved!

Hopefully this helps!