Question

[BRVR UHCAKIP]

biết \(cos\)α=\(\dfrac{-1}{4}\).Gía trị của biểu thức A =\(\dfrac{3sin\alpha-4cos\alpha}{2sin\alpha+3cos\alpha}\)bằng bao nhiêu?

Answer 1

[Sơn Mai Thanh Hoàng]

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

Biết tanα=\(-\dfrac{1}{4}\) nên ta có:

\(\dfrac{3\cdot\dfrac{-1}{4}-4}{2\cdot\dfrac{-1}{4}+3}=\dfrac{-\dfrac{3}{4}-4}{-\dfrac{1}{2}+3}=\dfrac{-19}{10}\)