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Question Number 185732 by Rupesh123 last updated on 26/Jan/23

Answered by witcher3 last updated on 26/Jan/23

$$\mathrm{tg}\left(\mathrm{a}\right)-\mathrm{tg}\left(\mathrm{b}\right)=\frac{\sin (\mathrm{a}-\mathrm{b})}{\cos \left(\mathrm{a}\right)\cos \left(\mathrm{b}\right)}$$$$\mathrm{tg}\left(50\right)-\mathrm{tg}\left(40\right)=\frac{\sin \left(10\right)}{\cos \left(40\right)\cos \left(50\right)}$$$$\iff \frac{\cos \left(10\right)}{\cos \left(40\right)\cos \left(50\right)}=\frac{\cos \left(10\right)}{\cos \left(40\right)\sin \left(40\right)}=2\frac{\cos \left(10\right)}{2\cos \left(40\right)\sin \left(40\right)}$$$$=\frac{2\cos \left(10\right)}{\sin \left(80\right)}=2$$

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