Question

Biết \(tan\)=\(\dfrac{1}{3}\). Gía trị công thức A= \(\dfrac{4sin\alpha+5cos\alpha}{2sin\alpha-3cos\alpha}\) bằng bao nhiêu?

Answer 1

\(\dfrac{4sin\alpha+5cos\alpha}{2sin\alpha-3cos\alpha}=\dfrac{\dfrac{4sin\alpha}{cos\alpha}+\dfrac{5cos\alpha}{cos\alpha}}{\dfrac{2sin\alpha}{cos\alpha}-\dfrac{3cos\alpha}{cos\alpha}}=\dfrac{4tan\alpha+5}{2tan\alpha-3}\)

Biết \(tan\)=\(\dfrac{1}{3}\) nên ta có:

\(\dfrac{4\times\dfrac{1}{2}+5}{2\times\dfrac{1}{2}-3}=\dfrac{2+5}{2-3}=\dfrac{7}{-2}=\dfrac{-7}{2}\)