Áp dụng \(cosa=sin\left(90^0-a\right)\) ta được:
\(A=\left(sin1+sin2+...+sin89\right)-\left(sin89+sin88+...+sin2+sin1\right)\)
\(=\left(sin1-sin1\right)+\left(sin2-sin2\right)+...+\left(sin89-sin89\right)=0\)
Áp dụng \(tana=cot\left(90^0-a\right)\)
\(B=tan1.tan89.tan2.tan88...tan44.tan46.tan45\)
\(=tan1.cot1.tan2.cot2...tan44.cot44.1=1.1...1=1\)
\(C=cot1.cot89.cot2.cot88...cot44.cot46.cot45\)
\(=cot1.tan1.cot2.tan2...cot44.tan44.cot45=1.1...1=1\)
\(D=sin^21+sin^289+sin^22+sin^288+...+sin^244+sin^246+sin^245\)
\(=sin^21+cos^21+sin^22+cos^22+...+sin^244+cos^244+\left(\dfrac{\sqrt{2}}{2}\right)^2\)
\(=1+1+...+1+\dfrac{1}{2}=44+\dfrac{1}{2}=\dfrac{89}{2}\)
