Question

6. Есептеңдер:
sin15º cos7º -cos11ºcos79°-sin4°sin86°


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Answer 1

$\displaystyle\bf\\Sin15^\circ Cos7^\circ-Cos11^\circ Cos79^\circ-Sin4^\circ Sin86^\circ=\\\\\\=Sin15^\circ Cos7^\circ-Cos11^\circ Cos(90^\circ-11^\circ)-Sin4^\circ Sin(90^\circ-4^\circ)=\\\\\\=Sin15^\circ Cos7^\circ-Cos11^\circ Sin11^\circ-Sin4^\circ Cos4^\circ=\\\\\\=\frac{1}{2} \Big[Sin(15^\circ-7^\circ)+Sin(15^\circ+7^\circ)\Big]-\frac{1}{2}Sin22^\circ-\frac{1}{2} Sin8^\circ =\\\\\\=\frac{1}{2}Sin8^\circ+\frac{1}{2} Sin22^\circ -\frac{1}{2}Sin22^\circ-\frac{1}{2} Sin8^\circ =0$