Câu 110:
\(B=\dfrac{2\cdot sin^230^0}{1-2\cdot cos^230^0}+4\cdot sin60^0-cot30^0\)
\(=\dfrac{2\cdot\left(\dfrac{1}{2}\right)^2}{1-2\cdot\left(\dfrac{\sqrt{3}}{2}\right)^2}+4\cdot\dfrac{\sqrt{3}}{2}-\sqrt{3}\)
\(=\dfrac{2\cdot\dfrac{1}{4}}{1-2\cdot\dfrac{3}{4}}+2\sqrt{3}-\sqrt{3}\)
\(=\dfrac{1}{2}:\left(1-\dfrac{3}{2}\right)+\sqrt{3}=\dfrac{1}{2}:\left(-\dfrac{1}{2}\right)+\sqrt{3}=\sqrt{3}-1\)
Câu 111:
\(T=tan1\cdot tan2\cdot...\cdot tan89\)
\(=\left(tan1\cdot tan89\right)\cdot\left(tan2\cdot tan88\right)\cdot...\cdot\left(tan44\cdot tan46\right)\cdot tan45\)
\(=\left(tan1\cdot cot1\right)\cdot\left(tan2\cdot cot2\right)\cdot...\cdot\left(tan44\cdot cot44\right)\cdot1\)
=1
Câu 112:
\(C=sin^251^0+sin^255^0+sin^239^0+sin^235^0\)
\(=\left(sin^251^0+sin^239^0\right)+\left(sin^255^0+sin^235^0\right)\)
\(=\left(sin^251^0+cos^251^0\right)+\left(sin^255^0+cos^255^0\right)\)
=1+1
=2
