​If $$(1+\text{tan}a)(1+\text{tan}\space4a)=2, a\space∈(0,\frac{π}{16})$$​ then $$a$$ is equal to:​

Correct option is C

Given:
The equation:
​$$(1 + \tan a)(1 + \tan 4a) = 2$$​​
where a $$\in \left(0, \frac{\pi}{16}\right)$$​
Concept Used:

(1 + tanA)(1 + tanB) =2

then, A + B =$$\frac{\pi}{4}$$​​

Solution:

$$(1 + \tan a)(1 + \tan 4a) = 2$$

$$a$$​+ 4$$a$$​ = $$\frac{\pi}{4}$$

5 $$a$$​=$$\frac{\pi}{4}$$

$$a$$​ =$$\frac{\pi}{20}$$$$\in \left(0, \frac{\pi}{16}\right)$$​​​

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