Verify that each trigonometric equation is an identity tan^2+1/sec α =sec α

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x=-16 ,y=17 when x squared -4y squared

To verify that the trigonometric equation tan^2 α + 1/sec α = sec α is an identity, we need to simplify the left side of the equation and show that it is equal to the right side for all possible values of α.

Let's start by simplifying the left side of the equation:

tan^2 α + 1/sec α

Using the identity tan^2 α + 1 = sec^2 α, we can rewrite the left side of the equation as:

sec^2 α/sec α

Now, let's simplify further by canceling out the sec α:

= sec α

Since the left side simplifies to sec α, and the right side is also sec α, we can conclude that the given equation is an identity.

Therefore, the trigonometric equation tan^2 α + 1/sec α = sec α is indeed an identity.