Tính giá trị các biểu thức sau:
1. A=\(\left(sin1^o+sin2^o+sin3^o+...+sin88^o+sin89^o\right)-\left(cos1^o+cos2^o+cos3^o+...+cos88^o+cos89^o\right)\)
2. B= \(\left(tan1^o.tan2^o.tan3^o...tan87^o.tan88^o.tan89^o\right)\)
3. C=\(cot1^o.cot2^o.cot3^o...tan87^o.tan88^o.tan89^o\)
4. D= \(sin^21^o+sin^22^o+sin^23^o+...+sin^287^o+sin^288^o+sin^289^o\)
5. E = \(cos^21^o+cos^22^o+cos^23^o+...+cos^287^o+cos^288^o+cos^289^o\)
4. \(D=sin^21^o+sin^22^o+sin^23^o+...+sin^287^o+sin^288^o+sin^289^o=\left(sin^21^o+sin^289^o\right)+\left(sin^22^o+sin^288^o\right)+...+\left(sin^244^o+sin^246^o\right)+sin^245^o=1+1+1+...+1+1+0,5=44,5\)
\(5.E=cos^21^o+cos^22^o+cos^23^o+...+cos^287^o+cos^288^o+cos^289^o=\left(cos^21^o+cos^289^o\right)+\left(cos^22^o+cos^288^o\right)+...+\left(cos^244^o+cos^246^o\right)+cos^245^o=1+1+1+...+1+0,5=1.44+0,5=44,5\)
mk bỏ dấu độ hết nha bn : (trong toán người ta cho phép)
1) ta có : \(A=\left(sin1+sin2+...+sin89\right)-\left(cos1+cos2+...+cos89\right)\)
\(=\left(sin1+sin2+...+sin89\right)-\left(cos\left(90-89\right)+cos\left(90-88\right)+...+cos\left(90-1\right)\right)\)
\(=\left(sin1+sin2+...+sin89\right)-\left(sin89+sin88+...+sin1\right)=0\)
2) ta có : \(B=tan1.tan2.tan3...tan87.tan88.tan89\)
\(=\left(tan1.tan89\right).\left(tan2.tan88\right).\left(tan3.tan87\right)...\left(tan44.tan46\right).tan45\)
\(=\left(tan1.tan\left(90-1\right)\right).\left(tan2.tan\left(90-2\right)\right).\left(tan3.tan\left(90-3\right)\right)...\left(tan44.tan\left(90-44\right)\right).tan45\)
\(=\left(tan1.cot1\right).\left(tan2.cot2\right).\left(tan3.cot3\right)...\left(tan44.cot44\right).tan45\) \(=tan45=1\)3) bạn xem lại đề nha
4) ta có : \(D=sin^21+sin^22+sin^23+...+sin^289\)
\(=\left(sin^21+sin^289\right)+\left(sin^22+sin^288\right)+...+\left(sin^244+sin^246\right)+sin^245\)
\(=\left(sin^21+sin^2\left(90-1\right)\right)+\left(sin^22+sin^2\left(90-2\right)\right)+...+\left(sin^244+sin^2\left(90-44\right)\right)+sin^245\)
\(=\left(sin^21+cos^21\right)+\left(sin^22+cos^22\right)+...+\left(sin^244+cos^244\right)+sin^245\)\(=44+sin^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)
5) ta có : \(E=cos^21+cos^22+cos^23+...+cos^289\)
\(=\left(cos^21+cos^289\right)+\left(cos^22+cos^288\right)+...+\left(cos^244+cos^246\right)+cos^245\)
\(=\left(cos^21+cos^2\left(90-1\right)\right)+\left(cos^22+cos^2\left(90-2\right)\right)+...+\left(cos^244+cos^2\left(90-44\right)\right)+cos^245\)
\(=\left(cos^21+sin^21\right)+\left(cos^22+sin^22\right)+...+\left(cos^244+sin^244\right)+cos^245\)\(=44+cos^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)
\(1.A=\left(sin1^o+sin2^o+sin3^o+...+sin88^o+sin89^o\right)-\left(cos1^o+cos2^o+cos3^o+...+cos88^o+cos89^o\right)=sin1^o+sin2^o+sin3^o+...+sin88^o+sin89^o-sin89^o-sin88^o-sin87^o-...-sin2^o-sin1^o=0\)
2.\(B=tan1^o.tan2^o.tan3^o...tan87^o.tan88^o.tan89^o\Rightarrow B=tan1^o.tan2^o.tan3^o...cot3^o.cot2^o.cot1^o=1^{45}=1\)
