Question

Show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x.

Answer 1

To Prove

tan 3x tan 2x tan x = tan 3x – tan 2 x – tan x.

Solution:

To prove: tan 3x tan 2x tan x = tan 3x – tan 2 x – tan x

We know that 3x can be written as 2x+x

Hence, tan 3x = tan (2x+x)

By using the trigonometric identity, the above expression is written as:Tan 3x = (tan 2x + tanx)/(1-tan 2x tanx)

Now, cross multiply above expression, we get

Tan 3x – tan 3x tan 2x tan x = tan 2x + tan x

Simplify the above equation, we get

tan 3x tan 2x tan x = tan 3x – tan 2x – tan x

Hence, tan 3x tan 2x tan x = tan 3x – tan 2x – tan x is proved.

Answer 2

$⟶tan(3x)−tan(2x)−tan(x)=tan(3x)tan(2x)tan(x)</p><p>\begin{gathered} \\ \: \: \: \: \: \: \: \: \: \underline{ \rm \green {\fbox{{Hence, Proved}}}} \\ \\ \end{gathered}</p><p>$