Question

Giải phương trình lượng giác

cos3x.cosx = cos2x

sinx.sin5x = sin2x.sin3x

Answer 1

a: \(\Leftrightarrow\dfrac{1}{2}\cdot\cos2x\cdot\cos x-\cos2x=0\)

\(\Leftrightarrow\cos2x=0\)

\(\Leftrightarrow2x=\dfrac{\Pi}{2}+k\Pi\)

hay \(x=\dfrac{\Pi}{4}+\dfrac{k\Pi}{2}\)

b: \(\Leftrightarrow\dfrac{1}{2}\cdot\left[\cos\left(5x-x\right)-\cos\left(5x+x\right)\right]=\dfrac{1}{2}\cdot\left[\cos\left(3x-2x\right)-\cos5x\right]\)

\(\Leftrightarrow\cos4x-\cos6x=\cos x-\cos5x\)

\(\Leftrightarrow x=\dfrac{\Pi}{2}+k\Pi\)