Sin (x- π/3)+sin(x-4π/3)=
inoid
![$\begin{align}\sin\left(x-\dfrac{\pi}3\right)+\sin\left(x-\dfrac{4\pi}3\right)&=\sin x\cos\dfrac{\pi}3-\cos x\sin\dfrac{\pi}3+\sin x\cos\dfrac{4\pi}3-\cos x\sin\dfrac{4\pi}3\\[4pt]&=\sin x\left(\dfrac12\right)-\cos x\left(\dfrac12\sqrt3\right)+\sin x\left(-\dfrac12\right)-\cos x\left(-\dfrac12\sqrt3\right)\\[4pt]&=\dfrac12\sin x-\dfrac12\sqrt3\cos x-\dfrac12\sin x+\dfrac12\sqrt3\cos x\\[4pt]&=0\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Csin%5Cleft%28x-%5Cdfrac%7B%5Cpi%7D3%5Cright%29%2B%5Csin%5Cleft%28x-%5Cdfrac%7B4%5Cpi%7D3%5Cright%29%26%3D%5Csin+x%5Ccos%5Cdfrac%7B%5Cpi%7D3-%5Ccos+x%5Csin%5Cdfrac%7B%5Cpi%7D3%2B%5Csin+x%5Ccos%5Cdfrac%7B4%5Cpi%7D3-%5Ccos+x%5Csin%5Cdfrac%7B4%5Cpi%7D3%5C%5C%5B4pt%5D%26%3D%5Csin+x%5Cleft%28%5Cdfrac12%5Cright%29-%5Ccos+x%5Cleft%28%5Cdfrac12%5Csqrt3%5Cright%29%2B%5Csin+x%5Cleft%28-%5Cdfrac12%5Cright%29-%5Ccos+x%5Cleft%28-%5Cdfrac12%5Csqrt3%5Cright%29%5C%5C%5B4pt%5D%26%3D%5Cdfrac12%5Csin+x-%5Cdfrac12%5Csqrt3%5Ccos+x-%5Cdfrac12%5Csin+x%2B%5Cdfrac12%5Csqrt3%5Ccos+x%5C%5C%5B4pt%5D%26%3D0%5Cend%7Balign%7D "$\begin{align}\sin\left(x-\dfrac{\pi}3\right)+\sin\left(x-\dfrac{4\pi}3\right)&=\sin x\cos\dfrac{\pi}3-\cos x\sin\dfrac{\pi}3+\sin x\cos\dfrac{4\pi}3-\cos x\sin\dfrac{4\pi}3\\[4pt]&=\sin x\left(\dfrac12\right)-\cos x\left(\dfrac12\sqrt3\right)+\sin x\left(-\dfrac12\right)-\cos x\left(-\dfrac12\sqrt3\right)\\[4pt]&=\dfrac12\sin x-\dfrac12\sqrt3\cos x-\dfrac12\sin x+\dfrac12\sqrt3\cos x\\[4pt]&=0\end{align}")
3 votes
Thanks 5
More Questions From This User See All
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
