3tan^4(x)-10tan^2(x)+3=0

Solution

3 tan^{4} (x) - 10 tan^{2} (x) + 3 = 0

x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

Solution steps

3 tan^{4} (x) - 10 tan^{2} (x) + 3 = 0

Solve by substitution

tan (x) = 3, tan (x) = - 3, tan (x) = \frac{1}{3}, tan (x) = - \frac{1}{3}

tan (x) = 3 : x = \frac{π}{3} + πn

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

tan (x) = \frac{1}{3} : x = arctan (\frac{1}{3}) + πn

tan (x) = - \frac{1}{3} : x = arctan (- \frac{1}{3}) + πn

Combine all the solutions

x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = arctan (\frac{1}{3}) + πn, x = arctan (- \frac{1}{3}) + πn

Show solutions in decimal form

x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

9 sec (x) csc (x) = 18 csc (x)

2 sin^{2} (x) = 2 - cos (x)

cos (x) = 0.25

- 2 sin (x) + sin (2 x) = 0

sin (x + \frac{π}{4}) = \frac{1}{2}