Question

Rút gọn:

A = sin²x +sin²\(\left(\dfrac{\pi}{3}-x\right)\) + sinxsin\(\left(\dfrac{\pi}{3}-x\right)\)

Answer 1

\(A=\dfrac{1-cos2x}{2}+\dfrac{1-cos\left(\dfrac{2\pi}{3}-2x\right)}{2}+\dfrac{1}{2}cos\left(2x-\dfrac{\pi}{3}\right)-\dfrac{1}{2}cos\left(\dfrac{\pi}{3}\right)\)

\(=\dfrac{3}{4}-\dfrac{1}{2}cos2x+\dfrac{1}{2}\left(cos\left(2x-\dfrac{\pi}{3}\right)-cos\left(\dfrac{2\pi}{3}-2x\right)\right)\)

\(=\dfrac{3}{4}-cos2x-sin\left(\dfrac{\pi}{6}\right).sin\left(2x-\dfrac{\pi}{2}\right)\)

\(=\dfrac{3}{4}-cos2x+cos2x=\dfrac{3}{4}\)