Multiply and simplify tan x cot x2SolutionGiven tanx cotx2

Multiply and simplify (tan x + cot x)^2.

Solution

Given (tanx + cotx)².

Need to multiply and simplify given expression.

(tanx + cotx)² = (tanx + cotx)*(tanx + cotx)

                      = tanx*(tanx + cotx) +cotx*(tanx + cotx)

                       = tanx*tanx +tanx* cotx + cotx*tanx + cotx*cotx

                       = tan²x + tanx* cotx + tanx*cotx + cot²x

                       = tan²x + 2tanx* cotx + cot²x

                       = tan²x + 2tanx* (1/tanx) + cot²x

                      = tan²x + 2 + cot²x

                       = tan²x + cot²x + 2

Therefore, (tanx + cotx)² = tan²x + cot²x + 2