Question

Решите в и г. Сколько сможете

Answer 1

27.1
в)cos²t-(cos²t-sin²t)=cos²t-cos²t+sin²t=sin²t
г)$frac{cos^{2}t-sin^{2}t }{cost-sint}-sint= frac{(cost-sint)(cost+sint)}{cost-sint}-sint=$=cost+sint-sint=cos t  
27.2
в)$frac{sin(2*50)}{2cos 50}= frac{2sin50*cos50}{2cos50}=sin50$
г)$frac{cos(2*18)+sin ^{2}18 }{cos18}= frac{cos ^{2}18-sin ^{2}18+sin ^{2}18 }{cos18}= frac{ cos^{2} 18}{cos18}=cos18$
27.3
в)cos²15-sin²15=cos(2*15)=cos30=√3/2
г)cos²15+2sin15*cos15+sin²15=1+sin(2*15)=1+sin30=1+1/2=1.5
27.4
в)$cos ^{2} frac{ pi }{8}-sin^{2} frac{ pi }{8} =cos frac{2* pi }{8}=cos frac{ pi }{4}= frac{ sqrt{2} }{2}$
г)$frac{ sqrt{2} }{2} -(cos ^{2} frac{ pi }{8} +2sin frac{ pi }{8} *cos frac{ pi }{8} +sin ^{2} frac{ pi }{8})= frac{ sqrt{2} }{2} -(1+sin frac{2* pi }{8})= frac{ sqrt{2} }{2} -1-sin frac{ pi }{4})$=-1
27.6
в) $2sint*cost* frac{cost}{sint}-1=2cos ^{2}t-sin ^{2}t -cos ^{2}t=cos ^{2}t-sin ^{2}t=cos2t$

Answer 2

спасибо