Question

if Φ is an acute angle and tanΦ + cotΦ=2,find the value of tan^5Φ+cot^5Φ​

Answer 1

Answer:

We are given that tanФ + cotФ = 2

tan⁵Ф + cot⁵Ф is to be found.

a⁵ + b⁵ = (a + b)(a⁴ - a³b + a²b² - ab³ + b⁴)

⇒ (tanФ + cotФ)(tan⁴Ф - tan³ФcotФ + tan²Фcot²Ф -tanФcot³Ф + cot⁴Ф)

⇒ (tanФ + cotФ)(tan⁴Ф + cot⁴Ф - tan²Ф - cot²Ф +1)

⇒ (tanФ + cotФ){tan²Ф(tan²Ф - 1) + cot²Ф(cot²Ф - 1) + 1}

⇒ 1/sinФcosФ x {(1 + sinФcosФ)/sin⁴Фcos⁴Ф} + 1

Answer 2

Answer:

refer to the above attachment for the solution