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If-3cosx-8sin-30-x-Find-tanx-




Question Number 205460 by hardmath last updated on 21/Mar/24
If  3cosx = 8sin(30° − x)  Find:  tanx = ?
$$\mathrm{If}\:\:\mathrm{3cosx}\:=\:\mathrm{8sin}\left(\mathrm{30}°\:−\:\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\mathrm{tanx}\:=\:? \\ $$
Answered by MM42 last updated on 21/Mar/24
3cosx=4cosx−4(√3)sinx  ⇒cosx=4(√3)sinx⇒tanx=((√3)/(12))  ✓
$$\mathrm{3}{cosx}=\mathrm{4}{cosx}−\mathrm{4}\sqrt{\mathrm{3}}{sinx} \\ $$$$\Rightarrow{cosx}=\mathrm{4}\sqrt{\mathrm{3}}{sinx}\Rightarrow{tanx}=\frac{\sqrt{\mathrm{3}}}{\mathrm{12}}\:\:\checkmark \\ $$

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