Question

 Упростить и вычислить

$4sin36^{o} * cos6^{o} + 4sin^{2}24^{o} -4$

Answer 1

4sin(90-54)*cos6 + 4sin^2(24) - 4=4cos54*cos6 + 4sin^2(24) - 4 =

=4*(1/2)*(cos48 + cos60) + 4sin^2(24) - 4 = 2cos48 +1 + 4sin^2(24) - 4 =

= 2cos^2(24) -2sin^2(24) + 1 + 4sin^2(24) - 4 = 2cos^2(24) +2sin^2(24) - 3 =

= 2 (cos^2(24) + sin^2(24)) - 3 = 2 - 3 = 1

Answer 2

2(sin(36+6)+sin(36-6)+2(1-cos48)-4=2sin42+2sin30+2-2cos48-4=

=2sin(90-48)+1+2-2cos48-4=2cos48+3-2cos48-4=-1