If cot ( P + Q) = 0 and tan ( P - Q) = $\frac{1}{\sqrt{3}}$, then what  is the value of ∠P and ∠Q ? (0 degree < P, Q ≤ 90 degree)

60 degree, 30 degree

We are given that ,

cot ( P + Q ) = 0

{ we know that , cot 90º = 0 }

So , P + Q = 90º    ----(1)

And tan ( P - Q ) = \(\frac{1}{√3}\)

{we know that , tan 30º = \(\frac{1}{√3}\) }

so, P - Q= 30º   ----(2)

On adding 1 and 2 equation,

2P = 90º

P = 60º

and Q = 90º - 60º

Q = 30º

Ans:- 45º & 30º