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3 years ago

Tan 235° = 2tan20°+ tan215°

Mathematics

1 answer:

Mariulka [41]3 years ago

5 0

Given : tan 235 = 2 tan 20 + tan 215

To Find : prove that

Solution:

tan 235 = 2 tan 20 + tan 215

Tan x = Tan (180 + x)

tan 235 = tan ( 180 + 55) = tan55

tan 215 = tan (180 + 35) = tan 35

=> tan 55 = 2tan 20 + tan 35

55 = 20 + 35

=> 20 = 55 - 35

taking Tan both sides

=> Tan 20 = Tan ( 55 - 35)

=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)

Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1

=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)

=> Tan 20 = (Tan 55 - Tan 35) /2

=> 2 Tan 20 = Tan 55 - Tan 35

=> 2 Tan 20 + Tan 35 = Tan 55

=> tan 55 = 2tan 20 + tan 35

=> tan 235 = 2tan 20 + tan 215

QED

Hence Proved

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Tan 235° = 2tan20°+ tan215°​

Tan 235° = 2tan20°+ tan215°