What is the general solution for arctan(3x)+arctan(x)= pi/4 ?

The general solution for arctan(3x)+arctan(x)= pi/4 is x=(sqrt(7)-2)/3

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arctan(3x)+arctan(x)= pi/4

arctan (3 x) + arctan (x) = \frac{π}{4}

x = \frac{7 - 2}{3}

Solution steps

arctan (3 x) + arctan (x) = \frac{π}{4}

Rewrite using trig identities

arctan (\frac{3 x + x}{1 - 3 xx}) = \frac{π}{4}

Apply trig inverse properties

\frac{3 x + x}{1 - 3 xx} = 1

Solve

\frac{3 x + x}{1 - 3 xx} = 1 : x = - \frac{2 + 7}{3}, x = \frac{7 - 2}{3}

x = - \frac{2 + 7}{3}, x = \frac{7 - 2}{3}

Verify solutions by plugging them into the original equation

x = \frac{7 - 2}{3}

4 sin (θ) = 3 sec (θ), 0 \leq θ < 18 0^{\circ}

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

\frac{2 cos ^{2} ( x )}{2 ( 1 - sin ( x ) ) - cos ^{2} ( x )} = 0

2 sin (x) = - 3

tan (θ) = \frac{- 12}{5}, cot (θ)

What is the general solution for arctan(3x)+arctan(x)= pi/4 ?
The general solution for arctan(3x)+arctan(x)= pi/4 is x=(sqrt(7)-2)/3