Question

 If tanA.tan4A=1 then find the value of A.​

Answer 1

Answer:

A = 18°

Step-by-step explanation:

$tanA.tan4A=1 \\ tanA= \frac{1}{tan4A} \\ tanA = cot4A \\ tanA = tan(90 - 4A) \\ A = 90 - 4A \\ 5A = 90 \\ A = \frac{90}{5} = 18$

Also, we can generalize it

$tanA = tan(90 - 4A) \\ n\pi + A = 90 - 4A \\ 5A = 90 - n\pi \\ A = \frac{90 - n\pi}{5}$