Question

Evaluate tan A + cot A is equal to 2 ,find tan square A + cot square A

Answer 1

Given that

tanA + cotA = 2

Squaring both side, we get

(tanA + cotA)² = 4

tan²A + cot²A +2tanAcotA = 4         [ using (a+b)² = a² +b² +2ab ]

tan²A + cot²A +2tanA(1/tanA) = 4     [ since cotA = 1/tanA ]

tan²A + cot²A +2 = 4

tan²A + cot²A = 4 - 2

tan²A + cot²A = 2