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how to calculate tan 15 degree value

how to calculate tan 15 degree value
 

Grade:11

2 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
tan15=tan(45-30)
=(tan45-tan30)/1+tan45tan30
=(1-1/sqrt3)/1+1/sqrt3
=sqrt3-1)/sqrt3+1
=(sqrt3-1)(sqrt3-1)/2
=(4-2sqrt3)/2
=2-sqrt3
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
tan2\theta = \frac{2tan\theta }{1-tan^{2}\theta }
tan30 = \frac{2tan15 }{1-tan^{2}15 }
\frac{2tan15 }{1-tan^{2}15 } = \frac{1}{\sqrt{3}}
tan^{2}15+2\sqrt{3}tan15-1=0
tan15 = \frac{-2\sqrt{3}\pm \sqrt{12+4}}{2} = \frac{-2\sqrt{3}\pm 4}{2}
tan15 = \frac{4-2\sqrt{3}}{2} = 2-\sqrt{3}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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