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Question Number 183184 by Tawa11 last updated on 22/Dec/22

Commented by Tawa11 last updated on 22/Dec/22

Thanks sir. God bless you.

$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

Answered by mr W last updated on 22/Dec/22

x=tan^(−1) (((tan 10)/(tan 20 tan 40)))=30°

$${x}=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\:\mathrm{10}}{\mathrm{tan}\:\mathrm{20}\:\mathrm{tan}\:\mathrm{40}}\right)=\mathrm{30}° \\ $$

Commented by mr W last updated on 22/Dec/22

Commented by mr W last updated on 22/Dec/22

tan x=((BD)/(BC))=((a tan 10°)/(a tan 20° tan 40°))=((tan 10°)/(tan 20° tan 40°)) ⇒x=tan^(−1) (((tan 10°)/(tan 20° tan 40°)))=30°

$$\mathrm{tan}\:{x}=\frac{{BD}}{{BC}}=\frac{{a}\:\mathrm{tan}\:\mathrm{10}°}{{a}\:\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°}=\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°} \\ $$$$\Rightarrow{x}=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°}\right)=\mathrm{30}° \\ $$

Commented by Tawa11 last updated on 22/Dec/22

Wow, God bless you sir.

$$\mathrm{Wow},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Commented by Tawa11 last updated on 22/Dec/22

I don′t know how. BC = a tan 20 tan 40

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{how}. \\ $$$$\mathrm{BC}\:\:=\:\:\mathrm{a}\:\mathrm{tan}\:\mathrm{20}\:\mathrm{tan}\:\mathrm{40} \\ $$

Commented by manxsol last updated on 23/Dec/22

Commented by Tawa11 last updated on 23/Dec/22

Very clear now. God bless you sir.

$$\mathrm{Very}\:\mathrm{clear}\:\mathrm{now}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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