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!

How do you verify the identity 2-sec^2z=1-tan^2z2-sec^2z=1-tan^2z?