Kąt α jest ostry i sinα=[latex] frac{3}{4} [/latex]. Oblicz ile wynosi wartość wyrażenia : sinα*cosα(tgα - [latex] frac{1}{tg alpha } [/latex])

[latex]sin alpha *cos alpha (tg alpha - frac{1}{tg alpha } )= \ = sin alpha *cos alpha *( frac{sin alpha }{cos alpha } - frac{1}{ frac{sin alpha }{cos alpha } } ) = \ sin^2 alpha -sin alpha *cos alpha* frac{cos alpha }{sin alpha } = \ sin^2 alpha - cos^2 alpha = sin^2 alpha -1+sin^2 alpha = \ 2sin^2 alpha -1 \ =2* (frac{3}{4} )^2 - 1 = 2* frac{9}{16} -1 = frac{1}{8} [/latex]