a) \(A=\left(\right.sin⁡^23^{\circ}+sin⁡^287^{\circ}\left.\right)+\left(\right.sin⁡^215^{\circ}+sin⁡^275^{\circ}\left.\right)=\left(\sin^23^{\circ}+\cos^23^{\circ}\right)+\left(\sin^215^{\circ}+\cos^215^{\circ}\right)=1+1=2\)

b) \(B=\left(\right.cos⁡0^{\circ}+cos⁡180^{\circ}\left.\right)+\left(\right.cos⁡20^{\circ}+cos⁡160^{\circ}\left.\right)+\ldots+\left(\right.cos⁡80^{\circ}+cos⁡100^{\circ}\left.\right)=\left(\cos0^{\circ}-\cos0^{\circ}\right)+\left(\cos20^{\circ}-\cos20^{\circ}\right)+\cdots+\left(\cos80^{\circ}-\cos80^{\circ}\right)=0\)

c) C​=(tan5∘tan85∘)(tan15∘tan75∘)…(tan45∘tan45∘)

=(tan5∘cot5∘)(tan15∘cot5∘)…(tan45∘cot5∘)=1.​

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a) \(A = a^{2} \cdot 1 + b^{2} \cdot 0 + c^{2} \cdot \left(\right. - 1 \left.\right) = a^{2} - c^{2}\)

b) \(B=3-\left(\right.1\left.\right)^2+2\left(\frac{1}{2}\right)^2-3\left(\frac{\sqrt{2}}{2}\right)^2=1\)

c) \(C=sin⁡^245^{\circ}+3cos⁡^245^{\circ}-2\left(\right.sin⁡^250^{\circ}+sin⁡^240^{\circ}\left.\right)+4tan⁡55^{\circ}\cdot cot⁡55^{\circ}\)
\(C=\left(\frac{\sqrt{2}}{2}\right)^2+3\left(\frac{\sqrt{2}}{2}\right)^2-2\left(\right.sin⁡^250^{\circ}+cos⁡^240^{\circ}\left.\right)+4=\frac{1}{2}+\frac{3}{2}-2+4=4\)