Question

(Cos2пи/9*ctg^2пи/9 + sin2пи/9*ctgпи/9)*tg^2пи/9

Answer 1

$(cos frac{2 pi }{9}* ctg^{2} frac{ pi }{9} +sin frac{ 2pi }{9} *ctg frac{ pi }{9} ) tg^{2} frac{ pi }{9}=$$cos frac{2 pi }{9} * ctg^{2} frac{ pi }{9} * tg^{2} frac{ pi }{9}+sin frac{2 pi }{9}*ctg frac{ pi }{9} * tg^{2} frac{ pi }{9} =cos frac{2 pi }{9}$$+sin frac{2 pi }{9} *tg frac{ pi }{9}=cos frac{2 pi }{9} +2sin frac{ pi }{9}*cos frac{ pi }{9} *tg frac{ pi }{9} =$$cos frac{2 pi }{9} +2sin frac{ pi }{9} *sin frac{ pi }{9} = cos^{2} frac{ pi }{9} - sin^{2} frac{ pi }{9}+2 sin^{2} frac{ pi }{9}=$$cos^{2} frac{ pi }{9} + sin^{2} frac{ pi }{9} =1$