Question

Упростить и вычислить без мк
1+sin18°/(sin9°+cos9°) ²
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Answer 1

$\displaystyle\bf\\\frac{1+Sin18^\circ}{(Sin9^\circ+Cos9^\circ)^{2} } =\frac{1+Sin18^\circ}{Sin^{2}9^\circ+2Sin9^\circ Cos9^\circ+Cos^{2}9^\circ } =\\\\\\=\frac{1+Sin18^\circ}{\underbrace{(Sin^{2}9^\circ+Cos^{2}9^\circ)}_{1}+ \underbrace{2Sin9^\circ Cos9^\circ}_{Sin18^\circ} } =\frac{1+Sin18^\circ }{1+Sin18^\circ}=1$