What is the general solution for arctan(1/4 x)-pi-arctan(x/(100))=-pi ?

The general solution for arctan(1/4 x)-pi-arctan(x/(100))=-pi is x=0

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arctan(1/4 x)-pi-arctan(x/(100))=-pi

arctan (\frac{1}{4} x) - π - arctan (\frac{x}{100}) = - π

x = 0

Solution steps

arctan (\frac{1}{4} x) - π - arctan (\frac{x}{100}) = - π

Rewrite using trig identities

- π + arctan (\frac{\frac{1}{4} x - \frac{x}{100}}{1 + \frac{1}{4} x \frac{x}{100}}) = - π

Add

π

to both sides

- π + arctan (\frac{\frac{1}{4} x - \frac{x}{100}}{1 + \frac{1}{4} x \frac{x}{100}}) + π = - π + π

Simplify

arctan (\frac{\frac{1}{4} x - \frac{x}{100}}{1 + \frac{1}{4} x \frac{x}{100}}) = 0

Apply trig inverse properties

\frac{\frac{1}{4} x - \frac{x}{100}}{1 + \frac{1}{4} x \frac{x}{100}} = 0

Solve

\frac{\frac{1}{4} x - \frac{x}{100}}{1 + \frac{1}{4} x \frac{x}{100}} = 0 : x = 0

x = 0

Verify solutions by plugging them into the original equation

x = 0

\frac{cot ( x ) + \frac{1}{c o t ( x )}}{cos ( x )} = sec (x)

sec (θ) = 2, (tan (θ) - sin (θ))^{2} + (1 - cos (θ))^{2}

(1 + csc (A)) (1 - csc (A)) = - cot (A)

6 cos^{2} (3 x) - cos (3 x) - 2 = 0

cos (2 x) - 3 cos (x) + 1 = 0

What is the general solution for arctan(1/4 x)-pi-arctan(x/(100))=-pi ?
The general solution for arctan(1/4 x)-pi-arctan(x/(100))=-pi is x=0