A light beam reflects such that tan A + cot A = 5 and A is an acute angle. Find the value of tan³ A + cot³ A.
Show answer & explanation
Correct answer: C
Explanation
given :
tan A + cot A = 5
According to the formula:
a³ + b³ = (a + b)³ − 3ab(a + b)
tanA × cotA = 1
tan³A + cot³A
= (tanA + cotA)³ − 3(tanA cotA)(tanA + cotA)
= 5³ − 3(1)(5)
= 125 − 15
= 110