Question

If tan 2x . tan 4x = 1 then tan 3x

Answer 1

Given,

tan 2x . tan 4x = 1

To find,

The value of tan 3x

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

It is given that,

tan 2x . tan 4x = 1

tan 2x = 1/tan 4x

tan 2x = cot 4x [As, 1/tan x = cot x]

tan 2x = tan (90°-4x) [As, cot x = tan (90°-x)]

This implies that,

2x = 90°-4x

2x+4x = 90°

6x = 90°

x = 15°

So, the value of the given term will be :

» tan 3x = tan (3×15°) [Putting the derived value of x]

= tan 45°

= 1

(This will be considered as the final value of given term ie. tan 3x)

Hence, the value of tan 3x is 1