Question

giải pt 5\(\cos\)x - 2\(\sin\dfrac{x}{2}\)+7 =0

Answer 1

\(5cosx-2sin\dfrac{x}{2}+7=0\)

\(\Leftrightarrow5\left(1-2sin^2\dfrac{x}{2}\right)-2sin\dfrac{x}{2}+7=0\)

\(\Leftrightarrow5-10sin^2\dfrac{x}{2}-2sin\dfrac{x}{2}+7=0\)

\(\Leftrightarrow5sin^2\dfrac{x}{2}+sin\dfrac{x}{2}-6=0\)

\(\Leftrightarrow\left(sin\dfrac{x}{2}-1\right)\left(5sin\dfrac{x}{2}+6\right)=0\)

\(\Leftrightarrow sin\dfrac{x}{2}-1=0\)

\(\Leftrightarrow sin\dfrac{x}{2}=1\)

\(\Leftrightarrow\dfrac{x}{2}=\dfrac{\pi}{2}+k2\pi\)

\(\Leftrightarrow x=\pi+k2\pi\)