Diketahui tan A=⅓ tan B=¹/5 dengan A dan B sudut lancip hitunglah tan(2A+B) jawab

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Diketahui tan A=⅓ tan B=¹/5 dengan A dan B sudut lancip hitunglah tan(2A+B) jawab

Tan (2A+B)
=frac{tan 2 alpha + tan beta beta }{1-tan 2 alpha (tan beta)}
=frac{ frac{2tan alpha}{1- tan^{2} alpha} + tan beta }{1-frac{2tan alpha}{1- tan^{2} alpha} (tan beta)}
= frac{ frac{2( frac{1}{3})}{1- ( frac{1}{3})^{2}} + frac{1}{5}}{1-frac{2( frac{1}{3})}{1- ( frac{1}{3})^{2}}(frac{1}{5})}
= frac{ frac{ frac{2}{3}}{1- frac{1}{9}} + frac{1}{5}}{1-frac{ frac{2}{3}}{1- frac{1}{9}} (frac{1}{5})}
=frac{ frac{ frac{2}{3}}{frac{8}{9}} + frac{1}{5}}{1-frac{ frac{2}{3}}{frac{8}{9}} (frac{1}{5})}
=frac{ frac{18}{24} + frac{1}{5}}{1-frac{18}{24} (frac{1}{5})}
= frac{ frac{90+24}{120}}{1-frac{18}{120}}
=(frac{114}{120})( frac{120}{102}})
= frac{19}{17}

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