Cái này khỏi bấm máy đi bạn
\(A=sin\left(x+14^0\right)\cdot sin\left(x+74^0\right)+sin\left(x-76^0\right)\cdot sin\left(x-16^0\right)\)
\(=\dfrac{1}{2}\cdot\left[cos\left(x+14^0-x-74^0\right)-cos\left(x+14^0+x+74^0\right)\right]+\dfrac{1}{2}\cdot\left[cos\left(x-76^0-x+16^0\right)-cos\left(x-76^0+x-16^0\right)\right]\)
\(=\dfrac{1}{2}\left[cos\left(-60^0\right)-cos\left(2x+88^0\right)\right]+\dfrac{1}{2}\cdot\left[cos\left(-60^0\right)-cos\left(2x-92^0\right)\right]\)
\(=\dfrac{1}{2}\cdot cos60^0-\dfrac{1}{2}\cdot cos\left(2x+88^0\right)+\dfrac{1}{2}\cdot cos60^0-\dfrac{1}{2}\cdot cos\left(2x-92^0\right)\)
\(=cos60^0-\dfrac{1}{2}\left[cos\left(2x+88^0\right)-cos\left(2x-92^0\right)\right]\)
\(=\dfrac{1}{2}-\dfrac{1}{2}\cdot\left[-2\cdot\sin\left(\dfrac{2x+88^0+2x-92^0}{2}\right)\cdot sin\left(\dfrac{2x+88^0-2x+92^0}{2}\right)\right]\)
\(=\dfrac{1}{2}-\dfrac{1}{2}\cdot\left[-2\cdot sin\left(2x-2^0\right)\cdot sin\left(\dfrac{180^0}{2}\right)\right]\)
\(=\dfrac{1}{2}-\dfrac{1}{2}\cdot\left[-2\cdot sin\left(2x-2^0\right)\cdot sin90^0\right]\)
\(=\dfrac{1}{2}+\dfrac{1}{2}\cdot2\cdot sin\left(2x-2^0\right)=sin\left(2x-2^0\right)+\dfrac{1}{2}\)
