tan^4(x)-3tan^2(x)+1=0

Solution

tan^{4} (x) - 3 tan^{2} (x) + 1 = 0

x = 1.01722 \dots + πn, x = - 1.01722 \dots + πn, x = 0.55357 \dots + πn, x = - 0.55357 \dots + πn

Solution steps

tan^{4} (x) - 3 tan^{2} (x) + 1 = 0

Solve by substitution

tan (x) = \frac{3 + 5}{2}, tan (x) = - \frac{3 + 5}{2}, tan (x) = \frac{3 - 5}{2}, tan (x) = - \frac{3 - 5}{2}

tan (x) = \frac{3 + 5}{2} : x = arctan \frac{3 + 5}{2} + πn

tan (x) = - \frac{3 + 5}{2} : x = arctan - \frac{3 + 5}{2} + πn

tan (x) = \frac{3 - 5}{2} : x = arctan \frac{3 - 5}{2} + πn

tan (x) = - \frac{3 - 5}{2} : x = arctan - \frac{3 - 5}{2} + πn

Combine all the solutions

x = arctan \frac{3 + 5}{2} + πn, x = arctan - \frac{3 + 5}{2} + πn, x = arctan \frac{3 - 5}{2} + πn, x = arctan - \frac{3 - 5}{2} + πn

Show solutions in decimal form

x = 1.01722 \dots + πn, x = - 1.01722 \dots + πn, x = 0.55357 \dots + πn, x = - 0.55357 \dots + πn

tan (θ) = \frac{- 4}{- 1}

cos (2 x) - 7 cos (x) + 6 = 0

csc^{2} (x) = 2 + csc (x)

tan (θ) = \frac{5.4}{1.1}

6 cos (2 θ) + 3 = 0