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

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


Simplifying
(tan2x + 1)(cos2x + -1) = -1tan2x

Reorder the terms:
(1 + an2tx)(cos2x + -1) = -1tan2x

Reorder the terms:
(1 + an2tx)(-1 + cos2x) = -1tan2x

Multiply (1 + an2tx) * (-1 + cos2x)
(1(-1 + cos2x) + an2tx(-1 + cos2x)) = -1tan2x
((-1 * 1 + cos2x * 1) + an2tx(-1 + cos2x)) = -1tan2x
((-1 + 1cos2x) + an2tx(-1 + cos2x)) = -1tan2x
(-1 + 1cos2x + (-1 * an2tx + cos2x * an2tx)) = -1tan2x

Reorder the terms:
(-1 + 1cos2x + (acn2os2tx2 + -1an2tx)) = -1tan2x
(-1 + 1cos2x + (acn2os2tx2 + -1an2tx)) = -1tan2x

Reorder the terms:
(-1 + acn2os2tx2 + -1an2tx + 1cos2x) = -1tan2x
(-1 + acn2os2tx2 + -1an2tx + 1cos2x) = -1tan2x

Add 'an2tx' to each side of the equation.
-1 + acn2os2tx2 + -1an2tx + an2tx + 1cos2x = -1an2tx + an2tx

Combine like terms: -1an2tx + an2tx = 0
-1 + acn2os2tx2 + 0 + 1cos2x = -1an2tx + an2tx
-1 + acn2os2tx2 + 1cos2x = -1an2tx + an2tx

Combine like terms: -1an2tx + an2tx = 0
-1 + acn2os2tx2 + 1cos2x = 0

Solving
-1 + acn2os2tx2 + 1cos2x = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + acn2os2tx2 + 1 + 1cos2x = 0 + 1

Reorder the terms:
-1 + 1 + acn2os2tx2 + 1cos2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + acn2os2tx2 + 1cos2x = 0 + 1
acn2os2tx2 + 1cos2x = 0 + 1

Combine like terms: 0 + 1 = 1
acn2os2tx2 + 1cos2x = 1

Add '-1cos2x' to each side of the equation.
acn2os2tx2 + 1cos2x + -1cos2x = 1 + -1cos2x

Combine like terms: 1cos2x + -1cos2x = 0
acn2os2tx2 + 0 = 1 + -1cos2x
acn2os2tx2 = 1 + -1cos2x

Divide each side by 'cn2os2tx2'.
a = c-1n-2o-1s-2t-1x-2 + -1n-2t-1x-1

Simplifying
a = c-1n-2o-1s-2t-1x-2 + -1n-2t-1x-1

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