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

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


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

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

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

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

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

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

Reorder the terms:
(acen2o2prs2tvx2 + -1aen2oprtvx + 1ceo2prs2vx + -1eoprv) = -1tan2x
(acen2o2prs2tvx2 + -1aen2oprtvx + 1ceo2prs2vx + -1eoprv) = -1tan2x

Solving
acen2o2prs2tvx2 + -1aen2oprtvx + 1ceo2prs2vx + -1eoprv = -1an2tx

Solving for variable 'a'.

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

Add 'an2tx' to each side of the equation.
acen2o2prs2tvx2 + -1aen2oprtvx + 1ceo2prs2vx + an2tx + -1eoprv = -1an2tx + an2tx

Reorder the terms:
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + 1ceo2prs2vx + -1eoprv = -1an2tx + an2tx

Combine like terms: -1an2tx + an2tx = 0
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + 1ceo2prs2vx + -1eoprv = 0

Add '-1ceo2prs2vx' to each side of the equation.
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + 1ceo2prs2vx + -1ceo2prs2vx + -1eoprv = 0 + -1ceo2prs2vx

Combine like terms: 1ceo2prs2vx + -1ceo2prs2vx = 0
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + 0 + -1eoprv = 0 + -1ceo2prs2vx
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + -1eoprv = 0 + -1ceo2prs2vx
Remove the zero:
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + -1eoprv = -1ceo2prs2vx

Add 'eoprv' to each side of the equation.
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + -1eoprv + eoprv = -1ceo2prs2vx + eoprv

Combine like terms: -1eoprv + eoprv = 0
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + 0 = -1ceo2prs2vx + eoprv
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx = -1ceo2prs2vx + eoprv

Reorder the terms:
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + ceo2prs2vx + -1eoprv = -1ceo2prs2vx + ceo2prs2vx + eoprv + -1eoprv

Combine like terms: -1ceo2prs2vx + ceo2prs2vx = 0
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + ceo2prs2vx + -1eoprv = 0 + eoprv + -1eoprv
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + ceo2prs2vx + -1eoprv = eoprv + -1eoprv

Combine like terms: eoprv + -1eoprv = 0
acen2o2prs2tvx2 + -1aen2oprtvx + an2tx + ceo2prs2vx + -1eoprv = 0

The solution to this equation could not be determined.

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