Question

Biết \(\sin\alpha=\dfrac{5}{13}\)

tính : \(B=\dfrac{\cot\alpha-\cos\alpha}{\cos^3\alpha}\)

Answer 1

ta có : \(B=\dfrac{cot\alpha-cos\alpha}{cos^3\alpha}\) \(\left(đk:cosx\ne0\right)\)

\(\Leftrightarrow B=\dfrac{cos\alpha\left(\dfrac{1}{sin\alpha}-1\right)}{cos^3\alpha}\Leftrightarrow B=\dfrac{\dfrac{1}{sin\alpha}-1}{cos^2\alpha}\)

\(\Leftrightarrow B=\dfrac{\dfrac{1}{sin\alpha}-1}{1-sin^2\alpha}=\dfrac{\dfrac{13}{5}-1}{1-\left(\dfrac{5}{13}\right)^2}=\dfrac{169}{90}\)

vậy \(B=\dfrac{169}{90}\) khi \(sin\alpha=\dfrac{5}{13}\)