Question

giúp mik vs

p=\(\dfrac{3sin\alpha+4cot\alpha}{2sin\alpha-5cot\alpha}\)

Answer 1

\(P=\dfrac{3\cdot sin\alpha+4\cdot cot\alpha}{2\cdot sin\alpha-5\cdot cot\alpha}\)

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

\(=\dfrac{3sin^2\alpha+4\cdot cos\alpha}{2\cdot sin^2\alpha-5\cdot cos\alpha}=\dfrac{3\cdot\left(1-cos^2\alpha\right)+4\cdot cos\alpha}{2\cdot\left(1-cos^2\alpha\right)-5\cdot cos\alpha}\)

\(=\dfrac{-3\cdot cos^2\alpha+4\cdot cos\alpha+3}{-2\cdot cos^2\alpha-5\cdot cos\alpha+2}\)