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izharulhaq78
![\displaystyle \frac{\sin27+\sin63}{\cos138+\cos102}=\frac{\sin45[\cos0\cos18+\sin0\sin18)]}{[\cos180\cos60+\sin180\sin60)]\cos18}\\\frac{\sin27+\sin63}{\cos138+\cos102}=\frac{\sin45[\cos18)]}{[-\cos60]\cos18}\\\frac{\sin27+\sin63}{\cos138+\cos102}=-\frac{\sin45}{\cos60}\\\frac{\sin27+\sin63}{\cos138+\cos102}=-\frac{\frac{1}{2}\sqrt2}{\frac{1}{2}}\\\boxed{\boxed{\frac{\sin27+\sin63}{\cos138+\cos102}=-\sqrt2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7B%5Csin27%2B%5Csin63%7D%7B%5Ccos138%2B%5Ccos102%7D%3D%5Cfrac%7B%5Csin45%5B%5Ccos0%5Ccos18%2B%5Csin0%5Csin18%29%5D%7D%7B%5B%5Ccos180%5Ccos60%2B%5Csin180%5Csin60%29%5D%5Ccos18%7D%5C%5C%5Cfrac%7B%5Csin27%2B%5Csin63%7D%7B%5Ccos138%2B%5Ccos102%7D%3D%5Cfrac%7B%5Csin45%5B%5Ccos18%29%5D%7D%7B%5B-%5Ccos60%5D%5Ccos18%7D%5C%5C%5Cfrac%7B%5Csin27%2B%5Csin63%7D%7B%5Ccos138%2B%5Ccos102%7D%3D-%5Cfrac%7B%5Csin45%7D%7B%5Ccos60%7D%5C%5C%5Cfrac%7B%5Csin27%2B%5Csin63%7D%7B%5Ccos138%2B%5Ccos102%7D%3D-%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%5Csqrt2%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5Cboxed%7B%5Cboxed%7B%5Cfrac%7B%5Csin27%2B%5Csin63%7D%7B%5Ccos138%2B%5Ccos102%7D%3D-%5Csqrt2%7D%7D "\displaystyle \frac{\sin27+\sin63}{\cos138+\cos102}=\frac{\sin45[\cos0\cos18+\sin0\sin18)]}{[\cos180\cos60+\sin180\sin60)]\cos18}\\\frac{\sin27+\sin63}{\cos138+\cos102}=\frac{\sin45[\cos18)]}{[-\cos60]\cos18}\\\frac{\sin27+\sin63}{\cos138+\cos102}=-\frac{\sin45}{\cos60}\\\frac{\sin27+\sin63}{\cos138+\cos102}=-\frac{\frac{1}{2}\sqrt2}{\frac{1}{2}}\\\boxed{\boxed{\frac{\sin27+\sin63}{\cos138+\cos102}=-\sqrt2}}")
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