# Thread: solve x for tan and cot

1. ## solve x for tan and cot

Please help me to solve x:

tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)

2. Originally Posted by Nico
Please help me to solve x:

tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)
sin (3x - 10)/cos (3x - 10) = cos (x + 10)/sin (x + 10)

sin (3x - 10) sin (x +10) = cos (3x - 10) cos (x + 10)

0 = cos (3x - 10) cos (x + 10) - sin (3x - 10) sin (x +10)

0 = cos (3x - 10 + x + 10)

0 = cos 4x

4x = 90, 270

x = 22.5, 67.5

3. Originally Posted by Nico
Please help me to solve x:

tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)
Here is an easy way to get one of the solutions.

Since tangent and cotangent are cofunctions. It means that they differ by 90 degrees.

Thus the angle sum between the tangent and cotangent should be 90 degrees.

3x-10+x+10=90

4x=90

x=22.5