Question

given that tan A = 1/5 , find the value of tan2A, tan4A and tan ( 45 - 4A)

Answer 1

Answer:

Value of tan 2A = 5 / 12 , tan 4A = 120 / 119 and tan (45 - 4A) = -1 / 239

Step-by-step explanation:

We have to find value of tan 2A , tan 4A  and tan (45 - 4A)

We use the following results,

tan 2A = 2 tan A / ( 1- tan² A  )

           = 2(1/5) / 1 - (1/25)

           = (2/5) / (24/25)

           = ( 2 × 25 ) / ( 24 × 5 )

           = 5 / 12

tan 4A = (2tan 2A) / (1-2tan² 2A)

           = 2(5/12) / (1 - 25/144)

           = (5/6) / (119/144)

           = 120/119

tan (45 - 4A) = (tan 45 - tan 4A) / (1 + tan 45 × tan 4A)

                     = (1 - 120/119) / (1 + 1 × 120/119)

                     = (-1/119) / (239/119)

                     = -1 / 239