Question

If tanx+cotx=3 then show that tan^4x+cot^4x=47

Answer 1

Given tanx+cotx=3

To Prove =tan^4x+cot^4x=47

Solution :

Tanx+Cotx=3

Squaring on both sides, we get

[Tanx+Cotx]²=3²

Tan²x+Cot²x+2Tanx Cotx=9

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

Answer 2

Answer:

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