`19)`

`a)`

`sin 5a. cos 5a`

`=1/2.[sin (5a+5a)+sin(5a-5a)]`

`=1/2.sin 10a`

`b)`

`sin a. cosa.cos 2a. cos 4a`

`=1/2.sin 2a. cos 2a. cos 4a`

`=1/2. 1/2. sin 4a. cos 4a`

`=1/4. 1/2. sin 8a`

`=1/8. sin 8a`

`c)`

`cos^2\ x/2-sin^2\ x/2=cos (2. x/2)=cosx`

`d)`

`(cosalpha+sinalpha)^2-sin 2alpha`

`=cos^2alpha+2sinalphacosalpha+sin^2 alpha-sin 2alpha`

`=1+sin 2alpha-sin 2alpha`

`=1`

`a)`

`sin5a.cos5a`

`=1/2.[sin(5a-5a)+sin(5a+5a)]`

`=1/(2).sin10a`

`b)` `sina.cosa.cos2a.cos4a`

Áp dụng `sina.cosa=1/(2).sin 2a`

`=1/(2).sin2a.cos2a.cos4a`

`=1/(4).sin4a.cos4a`

`=1/(8).sin8a`

`c)` `cos^(2)(x/2)-sin^(2)(x/2)`

`=cos(2.(x)/2)`

`=cosx`

`d)` `(cos alpha+sin alpha)^2-sin2a`

`=sin^(2)alpha+cos^(2)alpha+2sinalpha.cosalpha-sin2a`

`=1+sin2a-sin2a`

`=1`