HOTS Zone : Sistem Persamaan Trigonometri
Tipe:
No.
Diketahui sistem persamaan:$\begin{cases}\sin\left(x+y\right)=1+\dfrac15\cos y\\[4pt]\sin\left(x-\right)=-1+\cos y\end{cases}$
dengan $0\lt y\lt\dfrac{\pi}2$. maka
- $\dfrac7{25}$
- $\dfrac7{24}$
- $-\dfrac7{25}$
- $-\dfrac7{24}$
- $-\dfrac{17}{25}$
ALTERNATIF PENYELESAIAN
\(\begin{aligned}
\sin\left(x+y\right)&=1+\dfrac15\cos y\\[4pt]\sin\left(x-\right)&=-1+\cos y&{\color{red}+}\\\hline
\sin\left(x+y\right)+\sin\left(x-\right)&=\dfrac65\cos y\\[4pt]
2\sin x\cos y&=\dfrac65\cos y\\[4pt]
\sin x&=\dfrac35
\end{aligned}\)
\(\begin{aligned} \cos 2x&=1-2\sin^2x\\ &=1-2\left(\dfrac35\right)^2\\[4pt] &=1-2\left(\dfrac9{25}\right)\\[4pt] &=1-\dfrac{18}{25}\\ &=\color{blue}\boxed{\boxed{\color{black}\dfrac7{25}}} \end{aligned}\)
\(\begin{aligned} \cos 2x&=1-2\sin^2x\\ &=1-2\left(\dfrac35\right)^2\\[4pt] &=1-2\left(\dfrac9{25}\right)\\[4pt] &=1-\dfrac{18}{25}\\ &=\color{blue}\boxed{\boxed{\color{black}\dfrac7{25}}} \end{aligned}\)
Jadi, $\cos2x=\dfrac7{25}$.
JAWAB: A
JAWAB: A
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