(sec(x)-1)(sec(x)+1)=tan^2(x)

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Solution for (sec(x)-1)(sec(x)+1)=tan^2(x) equation: 


Simplifying
(sec(x) + -1)(sec(x) + 1) = tan2(x)

Multiply ces * x
(cesx + -1)(sec(x) + 1) = tan2(x)

Reorder the terms:
(-1 + cesx)(sec(x) + 1) = tan2(x)

Multiply ces * x
(-1 + cesx)(cesx + 1) = tan2(x)

Reorder the terms:
(-1 + cesx)(1 + cesx) = tan2(x)

Multiply (-1 + cesx) * (1 + cesx)
(-1(1 + cesx) + cesx(1 + cesx)) = tan2(x)
((1 * -1 + cesx * -1) + cesx(1 + cesx)) = tan2(x)
((-1 + -1cesx) + cesx(1 + cesx)) = tan2(x)
(-1 + -1cesx + (1 * cesx + cesx * cesx)) = tan2(x)
(-1 + -1cesx + (1cesx + c2e2s2x2)) = tan2(x)

Combine like terms: -1cesx + 1cesx = 0
(-1 + 0 + c2e2s2x2) = tan2(x)
(-1 + c2e2s2x2) = tan2(x)

Multiply an2t * x
-1 + c2e2s2x2 = an2tx

Solving
-1 + c2e2s2x2 = an2tx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + c2e2s2x2 = 1 + an2tx

Combine like terms: -1 + 1 = 0
0 + c2e2s2x2 = 1 + an2tx
c2e2s2x2 = 1 + an2tx

Divide each side by 'e2s2x2'.
c2 = e-2s-2x-2 + ae-2n2s-2tx-1

Simplifying
c2 = e-2s-2x-2 + ae-2n2s-2tx-1

Reorder the terms:
c2 = ae-2n2s-2tx-1 + e-2s-2x-2

Reorder the terms:
-1ae-2n2s-2tx-1 + c2 + -1e-2s-2x-2 = ae-2n2s-2tx-1 + e-2s-2x-2 + -1ae-2n2s-2tx-1 + -1e-2s-2x-2

Reorder the terms:
-1ae-2n2s-2tx-1 + c2 + -1e-2s-2x-2 = ae-2n2s-2tx-1 + -1ae-2n2s-2tx-1 + e-2s-2x-2 + -1e-2s-2x-2

Combine like terms: ae-2n2s-2tx-1 + -1ae-2n2s-2tx-1 = 0
-1ae-2n2s-2tx-1 + c2 + -1e-2s-2x-2 = 0 + e-2s-2x-2 + -1e-2s-2x-2
-1ae-2n2s-2tx-1 + c2 + -1e-2s-2x-2 = e-2s-2x-2 + -1e-2s-2x-2

Combine like terms: e-2s-2x-2 + -1e-2s-2x-2 = 0
-1ae-2n2s-2tx-1 + c2 + -1e-2s-2x-2 = 0

The solution to this equation could not be determined.

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