Вычислить.cos18°cos63°+sin18°sin63°

Question

Вычислить.cos18°cos63°+sin18°sin63°

Answer 1

Cos18⁰cos63⁰+sin18⁰sin63⁰=
=1/2·[cos(18⁰-63⁰)+cos(18⁰+63⁰)]+1/2·[cos(18⁰-63⁰)-cos(18⁰+63⁰)]=
=cos(18⁰-63⁰)=cos(-45⁰)=cos45⁰=√2/2

Answer 2

Cos18°cos63°+sin18°sin63°=cos(18°- 63°)= cos(-45°)=cos 45°=√2/2