Prove that : Cot -1 3 + Cot-1 5 + Cot -17 + Cot-1 8 = Π/ - Maths - Inverse Trigonometric Functions

Question

Prove that :
Cot -1 3 + Cot-1 5 + Cot -17 +
Cot-1 8 = ​Π/ 4

Varun.Rawat · Accepted Answer

LHS = cot-13 + cot-1 5 + cot-1 7  + cot-1 8= tan-113 + tan-115 + tan-117 + tan-118=tan-113 + tan-115 + tan-117 + tan-118=tan-113+151 - 13
15 + tan-117+181 - 17
18= tan-18/1514/15 + tan-115/5655/56=tan-147 + tan-1311=tan-147+3111 - 47
311=tan-165/7765/77=tan-11=tan-1tanπ4=π4=RHS

Prove that : Cot -1 3 + Cot-1 5 + Cot -17 + Cot-1 8 = ​Π/ 4

Prove that :
Cot ^-13 + Cot^-1 5 + Cot ^-17 + Cot^-1 8 = Π/ 4