Toán Biến đổi thành tích biểu thức: C= cosx.cos2x+ sin7x.sinx 19/09/2021 By Samantha Biến đổi thành tích biểu thức: C= cosx.cos2x+ sin7x.sinx
Đáp án: $\begin{array}{l}C = \cos x.\cos 2x + \sin 7x.\sin x\\ = \dfrac{1}{2}.2.\cos \dfrac{{3x – x}}{2}.\cos \dfrac{{3x + x}}{2}\\ + \dfrac{1}{2}.2.\sin \dfrac{{8x + 6x}}{2}.sin\dfrac{{8x – 6x}}{2}\\ = \dfrac{1}{2}.cos\left( {3x + x} \right) – \dfrac{1}{2}.\cos \left( {8x – 6x} \right)\\ = \dfrac{1}{2}.\cos 4x – \dfrac{1}{2}.\cos 2x\\ = \dfrac{1}{2}.\left( {\cos 4x – \cos 2x} \right)\\ = \dfrac{1}{2}.\left( {2{{\cos }^2}2x – 1 – \cos 2x} \right)\\ = \dfrac{1}{2}.\left( {2\cos 2x + 1} \right)\left( {\cos 2x – 1} \right)\end{array}$ Trả lời
Đáp án:
$\begin{array}{l}
C = \cos x.\cos 2x + \sin 7x.\sin x\\
= \dfrac{1}{2}.2.\cos \dfrac{{3x – x}}{2}.\cos \dfrac{{3x + x}}{2}\\
+ \dfrac{1}{2}.2.\sin \dfrac{{8x + 6x}}{2}.sin\dfrac{{8x – 6x}}{2}\\
= \dfrac{1}{2}.cos\left( {3x + x} \right) – \dfrac{1}{2}.\cos \left( {8x – 6x} \right)\\
= \dfrac{1}{2}.\cos 4x – \dfrac{1}{2}.\cos 2x\\
= \dfrac{1}{2}.\left( {\cos 4x – \cos 2x} \right)\\
= \dfrac{1}{2}.\left( {2{{\cos }^2}2x – 1 – \cos 2x} \right)\\
= \dfrac{1}{2}.\left( {2\cos 2x + 1} \right)\left( {\cos 2x – 1} \right)
\end{array}$