Prove that: tan 3x tan 2x tan x = tan 3x � tan 2 x � tan x

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.

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