Question

Вычислите (sinx+cosx):(2sinx-cosx), если tgx=1.25​

Answer 1

$dfrac{sin x+cos x}{2sin x-cos x}=dfrac{dfrac{sin x}{cos x} +dfrac{cos x}{cos x} }{dfrac{2sin x}{cos x} -dfrac{cos x}{cos x} }=dfrac{mathrm{tg},x+1}{2mathrm{tg},x-1}=dfrac{1.25+1}{2cdot1.25-1}=dfrac{2.25}{1.5}=1.5$