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Question Number 17921 by Tinkutara last updated on 12/Jul/17

$$\mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{expression}$$$$(3-{\tan }^{2}1°)(3-{\tan }^{2}2°)(3-{\tan }^{2}3°)....(3-{\tan }^{2}89°)$$$$\mathrm{is}\mathrm{equal}\mathrm{to}$$

Commented by Tinkutara last updated on 12/Jul/17

$$\mathrm{Thanks}\mathrm{Sir}!\mathrm{I}{\mathrm{didn}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{this}\mathrm{was}\mathrm{also}\mathrm{a}$$$$\mathrm{term}!$$

Commented by alex041103 last updated on 12/Jul/17

$$But...why???$$$$Canyouexplain,sir?$$

Commented by Tinkutara last updated on 12/Jul/17

$$3-{\tan }^{2}60°=3-{\left(\sqrt{3}\right)}^2=0\mathrm{and}\mathrm{it}\mathrm{is}$$$$\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{product}\mathrm{so}\mathrm{final}$$$$\mathrm{answer}\mathrm{is}0.$$

Commented by ajfour last updated on 12/Jul/17

$$3-\tan {}^{2}60°=0$$

Commented by alex041103 last updated on 12/Jul/17

$$thankyousir$$

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