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Category: Trigonometry

4-arctan-1-5-arctan-1-239-

Question Number 126499 by liberty last updated on 21/Dec/20 4arctan(15)arctan(1239)=? Answered by benjo_mathlover last updated on 21/Dec/20 letx=tan1(15)tanx=15$$\:\mathrm{tan}\:\mathrm{2}{x}=\frac{\mathrm{2tan}\:{x}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} {x}}\:=\:\frac{\mathrm{2}/\mathrm{5}}{\mathrm{1}−\mathrm{1}/\mathrm{25}}\: \

arctan-1-arctan-2-arctan-3-

Question Number 126381 by liberty last updated on 20/Dec/20 arctan1+arctan2+arctan3=? Answered by benjo_mathlover last updated on 20/Dec/20 ()arctan1+arctan2=arctan(1+211.2)arctan(3)$$\left(\bullet\bullet\right)\:\mathrm{arctan}\:\left(−\mathrm{3}\right)+\mathrm{arctan}\:\left(\mathrm{3}\right)=\mathrm{arctan}\:\left(\frac{−\mathrm{3}+\mathrm{3}}{\mathrm{1}−\left(−\mathrm{3}\right)\left(\mathrm{3}\right)}\right) \