What is the general solution for pi/4 =arctan(t) ?

The general solution for pi/4 =arctan(t) is t=1

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pi/4 =arctan(t)

\frac{π}{4} = arctan (t)

t = 1

Solution steps

\frac{π}{4} = arctan (t)

Switch sides

arctan (t) = \frac{π}{4}

Apply trig inverse properties

arctan (t) = \frac{π}{4}

arctan (x) = a \Rightarrow x = tan (a)

t = tan (\frac{π}{4})

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

t = 1

t = 1

sin (2 x) sin (x) cos (x) = 0

sin (4 x) - cos (4 x) = sin (2 x) - cos (2 x)

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

sin^{2} (\frac{x}{2}) = sin^{2} (x)

tan (θ) = \frac{220}{370}

What is the general solution for pi/4 =arctan(t) ?
The general solution for pi/4 =arctan(t) is t=1