If tan⁡x2=tan⁡y3=tan⁡z5 and x+y+z=π then the value of tan2⁡x+tan2⁡y+tan2⁡z is

x+y+z=π⇒tan⁡x+tan⁡y+tan⁡z=tan⁡ xtan⁡ ytan⁡ z ⇒2k+3k+5k=2k×3k×5k⇒k2=1/3tan2⁡x+tan2⁡y+tan2⁡z=13(4+9+25)=383.

If tan⁡x2=tan⁡y3=tan⁡z5 and x+y+z=π then the value of tan2⁡x+tan2⁡y+tan2⁡z is

x+y+z=π⇒tan⁡x+tan⁡y+tan⁡z=tan⁡ xtan⁡ ytan⁡ z ⇒2k+3k+5k=2k×3k×5k⇒k2=1/3tan2⁡x+tan2⁡y+tan2⁡z=13(4+9+25)=383.

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If $\frac{\tan x}{2} = \frac{\tan y}{3} = \frac{\tan z}{5}$ and $x + y + z = π$ then the value of $\tan^{2} x + \tan^{2} y + \tan^{2} z$ is

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$\frac{38}{3}$

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$x + y + z = π \Rightarrow \tan x + \tan y + \tan z =$ $\tan x \tan y \tan z$

$\Rightarrow 2 k + 3 k + 5 k = 2 k \times 3 k \times 5 k \Rightarrow k^{2} = 1 / 3$

$\tan^{2} x + \tan^{2} y + \tan^{2} z = \frac{1}{3} (4 + 9 + 25) = \frac{38}{3}$ .

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If tan⁡x2=tan⁡y3=tan⁡z5 and x+y+z=π then the value of tan2⁡x+tan2⁡y+tan2⁡z is

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If $\frac{\tan x}{2} = \frac{\tan y}{3} = \frac{\tan z}{5}$ and $x + y + z = π$ then the value of $\tan^{2} x + \tan^{2} y + \tan^{2} z$ is