Question

Tính giá trị biểu thức: \(\cos12^0+\cos18^0-4\times\cos15^0\times\cos21^0\times\cos24^0\)

Answer 1

Answer 2

\(=2.cos\dfrac{12^o+18^o}{2}.cos\dfrac{12-18^o}{2}-4.cos15^o.\dfrac{cos\left(21^o-24^o\right)+cos\left(21^o+24^o\right)}{2}\)
\(=2.cos15^o.cos\left(-3^o\right)-2.cos15^o.\left(cos\left(-3^o\right)+cos45^o\right)\)
\(=2.cos15^o.cos3^o-2.cos15^0.\left(cos3^o+\sqrt{2}\right)\)
\(=2.cos15^o.cos3^o-2.cos15^o.cos3^o-2\sqrt{2}.cos15^o\)
\(=-2\sqrt{2}.cos15^o\)