Question

If tanx,tan3x =1 ,then tan2x is

Answer 1

Answer:

tanx.tan3x=1

tan3x=1/tanx

tan3x=cotx

tan3x=tan(90°-x)

3x=90°-x

4x=90°

x=22.5°

then

tan2x=tan(2×22.5)

tan2x=tan45°

tan2x= 1√√√√√

Answer 2

Answer:

tan2x = 2

Step-by-step explanation:

From the above question,

They have given :

Given, tanx = tan3x = 1.

From the identity tan2x = (2 tanx) / (1 - $tan^2$ x),

we get tan2x = (2) / (1 - 1) = 2.

When tanx = tan3x = 1, it means that x and 3x are equal to an angle in the first quadrant whose tangent is equal to 1. Let's call this angle θ.

Since x = θ, then 3x = 3θ, and 2x = 2θ.

Now, to find tan2x, we can use the identity: tan2θ = 2tanθ / (1 - tan^2θ). In this case, tanθ = 1, so the expression becomes: tan2θ = 2tanθ / (1 - $1^2$) = 2 * 1 / (0) = undefined.

So the value of tan2x is undefined when tanx = tan3x = 1.

Therefore, tan2x = 2.

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