Question

Find the angle θ in the following, if 0° < θ < 90°.

tan `θ/2 = cot 2θ`

Answer 1

cot x = tan (90° − x)

tan `θ/2` = cot 2θ

Replace cot ⁡2θ with tan ⁡(90° − 2θ):

tan `θ/2` = tan (90° − 2θ)

For 0° < θ < 90° we can equate angles:

`θ/2 = 90° − 2θ`

`θ/2​ + 2θ = 90°`

`(θ + 40)/2 = 90°`

`(θ + 4θ​)/2 = 90°`

`(5θ)/2​ = 90°`

θ = 36°