Question

tanx+cotx=3 then tan^4x+cot^4x=​

Answer 1

Tan²X+Cot²X +2=9 [Since Tanxcotx=1]

Tan²X+Cot²X =7

Squaring on both sides ,

[Tan²X+Cot²X ]²=7²

Tan⁴X+Cot⁴X+2Tan²X.cot²X=49

Tan⁴X+Cot⁴X+2=49

∴Tan⁴X+Cot⁴X=47

Hence proved