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Trignometry

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4 Apr 2008 22:27:18 IST

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Explain the steps in the process

None

Please calculate the value of

tan 37.5⁰

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sreeraman nagasubramaniyan

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4 Apr 2008 23:02:37 IST

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$\tan(75) = \tan(45+30) = \frac{\sqrt{3}+1}{\sqrt{3}-1} \\ \\ \tan(\frac{75}{2}) = t \\ \\ \Rightarrow \frac{2t}{1-t^2} = \frac{\sqrt{3}+1}{\sqrt{3}-1} \\ \\ \Rightarrow t^2(\sqrt{3}+1)+2t(\sqrt{3}-1)-(\sqrt{3}+1) = 0 \\ \\ \Rightarrow t=\sqrt{3}+\sqrt{6}-\sqrt{2}-2 \\ \\ \Rightarrow \tan(37.5) = \sqrt{3}+\sqrt{6}-\sqrt{2}-2$

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