Given,

A + B = 90°

B = 90° - A

Putting this Value in the given equation we get,

∵ tan (90 – A) = Cot A sin(90 – A) = cos A

cot (90 – A) = tan A

sec (90 – A) = cosec A

[∵ cot A = 1/tan A and cosec A = 1/sin A]

⇒ 1 + tan² A – 1

∵ A + B = 90°

A = 90 – B

So,

⇒ tan²(90 – B)

⇒ cot²B