What is the general solution for (1+tan(t))/(sin(t))=0 ?

The general solution for (1+tan(t))/(sin(t))=0 is t=(3pi)/4+pin

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(1+tan(t))/(sin(t))=0

\frac{1 + tan ( t )}{sin ( t )} = 0

t = \frac{3 π}{4} + πn

Degrees

t = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

\frac{1 + tan ( t )}{sin ( t )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + tan (t) = 0

Move

1

to the right side

1 + tan (t) = 0

Subtract

1

from both sides

1 + tan (t) - 1 = 0 - 1

Simplify

tan (t) = - 1

tan (t) = - 1

General solutions for

tan (t) = - 1

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}

t = \frac{3 π}{4} + πn

t = \frac{3 π}{4} + πn

What is the general solution for (1+tan(t))/(sin(t))=0 ?
The general solution for (1+tan(t))/(sin(t))=0 is t=(3pi)/4+pin