Question

If tanx-cotx=5 then what is the value of tan²x+cot²x​

Answer 1

27

Explanation:

note that tanx cotx = tanx ×
`(1)/(tanx)` = 1

Given

tanx - cotx = 5 ( square both sides )

(tanx - cotx)² = 5² = 25 ← expand left side using FOIL

tan²x - 2tanxcotx + cot²x = 25

tan²x - 2 + cot²x = 25 ( add 2 to both sides )

tan²x + cot²x = 27