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AonZ
 2 years ago
Given t = tan112.5, show that 2t / 1t^2 = 1
hence show that tan112.5 = sqrt(2)  1
AonZ
 2 years ago
Given t = tan112.5, show that 2t / 1t^2 = 1 hence show that tan112.5 = sqrt(2)  1

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dan815
 2 years ago
Best ResponseYou've already chosen the best response.0use tan trig identity itll simpify

surjithayer
 2 years ago
Best ResponseYou've already chosen the best response.1\[\tan 2t=\frac{2\tan t }{1\tan ^{2} t },put t=112.5\] tan2t=tan(112.5)*2=tan225=tan(180+45)=tan45=1 \[\frac{ 2\tan t }{1\tan ^{2}t }=\1\] \[\frac{ 2t }{1t ^{2} }=1\] 2t=1t^2 \[t ^{2}+2t1=0,t=\frac{ 2\pm \sqrt{2^{2}4\left( 1 \right)\left( 1 \right)} }{2\times1}\] \[t=\frac{ 2\pm \sqrt{8} }{2 }=\frac{ 1\pm \sqrt{2} }{ 1 }\] in the second quadrant tan is negative. \[Hence \tan112.5=1\sqrt{2}\]
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