Verify that each equation is an identity?

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Verify that each equation is an identity?

(sec a - tan a)(sec a + tan a) = 1

1 Answer

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Answer 1 · 2016-11-29T19:14:10

Multiply out the brackets and then apply the Pythagorean Identity ${tan}^{2} (x) + 1 = {sec}^{2} (x)$ $Tan^2(x) + 1 = Sec^2(x)$

Explanation:

Left Side = (SecA - TanA)(SecA + TanA)
= ${sec}^{2} A + sec A tan A - tan A sec A - {tan}^{2} A$ $Sec^2A + SecATanA - TanASecA - Tan^2A$

Notice that $sec A tan A - tan A sec A = 0$ $SecATanA - TanASecA = 0$

So Left Side = ${sec}^{2} A - {tan}^{2} A$ $Sec^2A - Tan^2A$

Now apply the Pythagorean Identity ${tan}^{2} A + 1 = {sec}^{2} A$ $Tan^2A + 1 = Sec^2A$ by replacing the ${sec}^{2} A$ $Sec^2A$ by ${tan}^{2} A + 1$ $Tan^2A + 1$

Left Side = ${tan}^{2} A + 1 - {tan}^{2} A$ $Tan^2A + 1 - Tan^2A$

Left Side = 1

Left Side = Right Side [Q.E.D.]

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Verify that each equation is an identity?

(sec a - tan a)(sec a + tan a) = 1

1 Answer

Explanation:

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