Question

If tan2A×tan4A=1 then find the value of tan3A

Answer 1

The step-by-step solution for your problem is as follows.


tan(x - y) = (tan x - tan y) / (1 + tan x tan y) , so

tan(4A - 2A) = (tan 4A - tan 2A) / (1 + tan 4A * tan 2A)
tan 2A = (tan 4A - tan 2A) / 2 ; as tan 4A * tan 2A = 1
2 tan (2A) = tan (4A) - tan (2A)
3 tan (2A) = tan (4A)

plug this value to original equation tan (2A) * tan (4A) = 1, we get
tan (2A) * 3 tan (2A) = 1
tan² (2A) = 1/3
tan (2A) = 1/√3
2A = 30°
=>A = 15°
therefore 3A = 45°, and tan (3A) = tan (45°) = 1

tan(3A) = 1.

Hope it answers your question.
All the best!
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