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Simplifying Tan(x + 45) = 8tanx Reorder the terms: anT(45 + x) = 8tanx (45 * anT + x * anT) = 8tanx (45anT + anxT) = 8tanx Solving 45anT + anxT = 8antx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8antx' to each side of the equation. 45anT + -8antx + anxT = 8antx + -8antx Combine like terms: 8antx + -8antx = 0 45anT + -8antx + anxT = 0 Factor out the Greatest Common Factor (GCF), 'an'. an(45T + -8tx + xT) = 0Subproblem 1
Set the factor 'an' equal to zero and attempt to solve: Simplifying an = 0 Solving an = 0 Move all terms containing a to the left, all other terms to the right. Simplifying an = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(45T + -8tx + xT)' equal to zero and attempt to solve: Simplifying 45T + -8tx + xT = 0 Solving 45T + -8tx + xT = 0 Move all terms containing a to the left, all other terms to the right. Add '-45T' to each side of the equation. 45T + -8tx + -45T + xT = 0 + -45T Reorder the terms: 45T + -45T + -8tx + xT = 0 + -45T Combine like terms: 45T + -45T = 0 0 + -8tx + xT = 0 + -45T -8tx + xT = 0 + -45T Remove the zero: -8tx + xT = -45T Add '8tx' to each side of the equation. -8tx + 8tx + xT = -45T + 8tx Combine like terms: -8tx + 8tx = 0 0 + xT = -45T + 8tx xT = -45T + 8tx Add '-1xT' to each side of the equation. xT + -1xT = -45T + 8tx + -1xT Combine like terms: xT + -1xT = 0 0 = -45T + 8tx + -1xT Simplifying 0 = -45T + 8tx + -1xT The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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