Question

Answer 1

3.

\(A=\dfrac{sin5a}{sina}-2\left(cos2a+cos4a\right)=\dfrac{sin5a}{sina}-4cos3a.cosa\)

\(=\dfrac{sin5a-4cosa.sina.cos3a}{sina}=\dfrac{sin5a-2sin2a.cos3a}{sina}\)

\(=\dfrac{sin5a-\left(sin5a-sina\right)}{sina}=\dfrac{sina}{sina}=1\)

4.

\(A=sin4x.sin10x-sin11x.sin3x-sin7x.sinx\)

\(=\dfrac{1}{2}\left(cos6x-cos14x\right)-\dfrac{1}{2}\left(cos8x-cos14x\right)-\dfrac{1}{2}\left(cos6x-cos8x\right)\)

\(=\dfrac{1}{2}cos6x-\dfrac{1}{2}cos6x-\dfrac{1}{2}cos14x+\dfrac{1}{2}cos14x-\dfrac{1}{2}cos8x+\dfrac{1}{2}cos8x=0\) (đpcm)