Question

If tan a+ cot a=4 then find the value of tan^4a+cot^4a=?​

Answer 1

Given

→ tanA + cotA = 4

Squaring both sides we get,

→ tan²A + cot²A + 2(tanA)(cotA) = 16

→ tan²A + cot²A + 2 = 16

→ tan²A + cot²A = 14

Squaring both sides we get,

→ tan⁴A + cot⁴A + 2(tan²A)(cot²A) = 196

→ tan⁴A + cot⁴A = 196 - 2

→tan⁴A + cot⁴A = 194

Answer: 194

Answer 2

Given

→ tanA + cotA = 4

Squaring both sides we get,

→ tan²A + cot²A + 2(tanA)(cotA) = 16

→ tan²A + cot²A + 2 = 16

→ tan²A + cot²A = 14

Squaring both sides we get,

→ tan⁴A + cot⁴A + 2(tan²A)(cot²A) = 196

→ tan⁴A + cot⁴A = 196 - 2

→tan⁴A + cot⁴A = 194

Answer: 194

Hope it helps you!!!