Question

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

Answer 1

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