<span>cos20°cos10°=(1/2)( cos(20°+10°)·cos(20°-10°))= (1/2)cos30°+(1/2)cos10°
Тогда
0,5·sin40°-cos30°+ cos20°·cos10°=
=</span><span>0,5·sin40°-cos30° +</span><span>(1/2)cos30°+(1/2)cos10°
=</span><span>0,5·sin40°+0,5сos10°-0,5cos30°=
=0,5sin40°+0,5·(cos10°-cos30°)=
=</span><span><span><span>0,5sin40°+0,5·2sin((10°+30°)/2)sin((30°-10°)/2)</span>
</span>
=0,5·2sin20°cos20°+sin20°·sin10°=
=sin20°·(cos20°+sin10°)</span>
10y-20=10y-20
0=0
бессмыслица...
Согласно таблице интегралов
![\int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}\frac{dx}{\sqrt{1-x^2}}=\arcsin x|_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}=](https://tex.z-dn.net/?f=%5Cint_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5E%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%5Cfrac%7Bdx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%3D%5Carcsin+x%7C_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5E%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%3D)
![=\arcsin \frac{\sqrt{3}}{2}-\arcsin \frac{1}{2}=\frac{\pi}{3}-\frac{\pi}{6}=\frac{\pi}{6}](https://tex.z-dn.net/?f=%3D%5Carcsin+%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D-%5Carcsin+%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%5Cpi%7D%7B3%7D-%5Cfrac%7B%5Cpi%7D%7B6%7D%3D%5Cfrac%7B%5Cpi%7D%7B6%7D)
Ответ:
![\frac{\pi}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B6%7D)