Question

Question : Trignometry solve fast

tanxtan2xtan3x = tan3x - tan2x - tanx ​​

Answer 1

Explanation:

We can use sum logic here

$\implies$ x + 2x = 3x

Now take tan both side

$\implies$ tan( x + 2x) = tan3x

Use Trignometric Identity as

$\implies$ tan(A + B) = $\frac{tanA + tanB}{1 - tanAtanB}$

$\implies$ tan(x + 2x) = tan3x

$\implies$ $\frac{tanx + tan2x }{1 - tanx × tan2x }$ = tan3x

Multiplying the denominat to the right side ,

$\implies$ tanx + tan2x =( tan3x) ×( 1 - tanx × tan2x )

$\implies$ tanx + tan2x = tan3x - tan3x Tanx Tan2x

Shifting the sides,

$\boxed{tanx Tan2x Tan3x = Tan3x - Tan2x - Tanx }$

Answer 2

Explanation:

hope it helps you !......................