What is the general solution for tan(x)tan(2x)=1 ?

The general solution for tan(x)tan(2x)=1 is x=0.52359…+pin,x=-0.52359…+pin

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tan(x)tan(2x)=1

tan (x) tan (2 x) = 1

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

Solution steps

tan (x) tan (2 x) = 1

Subtract

1

from both sides

tan (x) tan (2 x) - 1 = 0

Rewrite using trig identities

- 1 + \frac{2 tan ^{2} ( x )}{1 - tan ^{2} ( x )} = 0

Solve by substitution

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

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

Show solutions in decimal form

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

2 sin^{2} (x) + 7 sin (x) = 4

22 cos (θ) + 4 = 6

sin (x) + cos (x) = \frac{1}{2}

6 sin^{2} (x) + 9 sin (x) + 3 = 0

cos^{2} (x) + 2 cos (x) - 1 = 0

What is the general solution for tan(x)tan(2x)=1 ?
The general solution for tan(x)tan(2x)=1 is x=0.52359…+pin,x=-0.52359…+pin