Explicație pas cu pas:
[tex] \cot( \alpha ) = \frac{4}{15} < = > \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = \frac{4}{15} \\ \cos( \alpha ) = \frac{4 \sin( \alpha ) }{15} [/tex]
notăm
[tex] \sin( \alpha ) = x = > \cos( \alpha ) = \frac{4x}{15} [/tex]
[tex]E( \alpha )= \frac{3 \sin( \alpha ) + 5 \cos( \alpha ) }{3 \cos( \alpha ) - 2 \sin( \alpha ) } [/tex]
=>
[tex]E(x) = \frac{3x + 5 \times \frac{4x}{15} }{3 \times \frac{4x}{15} - 2x } = \frac{(9x + 4x) \times 5}{(4x - 10x) \times 3} = \frac{13x \times 5}{ - 6x \times 3} = - \frac{65}{18}[/tex]
=>
[tex]\frac{3 \sin( \alpha ) + 5 \cos( \alpha ) }{3 \cos( \alpha ) - 2 \sin( \alpha ) } = - \frac{65}{18} [/tex]
