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Question Number 79437 by Vishal Sharma last updated on 25/Jan/20

$$\mathrm{The}\mathrm{value}\mathrm{of}\tan 1°\tan 2°\tan 3°...\tan 89°$$$$\mathrm{is}$$

Commented by mr W last updated on 25/Jan/20

$$=1$$$$since\tan \left(x\right)\times \tan (90-x)=1$$

Commented by mathmax by abdo last updated on 25/Jan/20

$$A=tan\left(\frac{\pi }{180}\right).tan\left(\frac{2\pi }{180}\right).....tan\left(\frac{89\pi }{180}\right)$$$$wehavetan\left(\frac{89\pi }{180}\right)=tan(\frac{\pi }{2}-\frac{\pi }{180})=\frac{1}{tan\left(\frac{\pi }{180}\right)}$$$$tan\left(\frac{88\pi }{180}\right)=tan(\frac{\pi }{2}-\frac{2\pi }{180})=\frac{1}{tan\left(\frac{2\pi }{180}\right)}....\Rightarrow A=1$$

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