Question

tan2a×tan4a= 1 then tan3a =?​

Answer 1

Answer:

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 

I hope it will help you

Answer 2

Answer:

tan (2A + A)

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