Ответ:      4 . ( 1/2)sin2x + √3/4 ;  5. 2cos2α .

Объяснение:

4 . sin( 30°+ x)cos(30° - x) = ( 1/2 )[ sin( 30°+ x - 30° +x ) + sin( 30°+ x+30°- x) ] =

=( 1/2)( sin2x + sin60°) =  ( 1/2)sin2x + ( 1/2)* (√3/2) = ( 1/2)sin2x + √3/4 ;

5 . ( cos5α + cosα )/( cos2αcosα - sin2αsinα )=

= (2cos3αcos2α )/ ( cos3α ) = 2cos2α .