4sin³α*cos3α+4cos³α*sin3α Упростите

Question

4sin³α*cos3α+4cos³α*sin3α Упростите

Answer 1

4 sin³α·cos3α+4cos³α·sin3α=4sin³α·(4cos³α-3cosα)+4cos³α·(3sinα-4sin³α)=
=16sin³α·cos³α-12sin³α·cosα+12sinα·cos³α-16cos³αsin³α=
=12sinαcosα(cos²α-sin²α)=6sin2α·cos2α=3sin4α