Задание:
Упростить cos^6 α+sin^6 α+3cos^2 α*sin^2 α
Решение:
cos^6 α+sin^6 α+3cos^2 α*sin^2 α=(cos^2 α+sin^2 α) (cos^4 α+sin^4 α -cos^2 α*sin^2 α)+3cos^2 α*sin^2 α=1*(cos^4 α+sin^4 α -cos^2 α*sin^2 α)+3cos^2 α*sin^2 α=cos^4 α+sin^4 α -cos^2 α*sin^2 α+3cos^2 α*sin^2 α=cos^4 α+sin^4 α+2cos^2 α*sin^2 α=(cos^2 α+sin^2 α) ^2=1
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