Question

Không dùng máy tính hãy tính:

A= \(Sin^25^o+Sin^225^o+Sin^245^o+Sin^265^o+Sin^285^o\)

B=\(tan1^o.tan2^o.tan3^o.......tan88^o.tan89^o\)

Answer 1

\(A=\left(\sin^25^0+\sin^285^0\right)+\left(\sin^225^0+\sin65^0\right)+\sin^245^0\)

\(=\left(\sin^25^0+\cos^25^0\right)+\left(\sin^225^0+\cos^225^0\right)+\frac{1}{2}\)

\(=1+1+\frac{1}{2}\)

\(=\frac{5}{2}\)

Answer 2

\(B=\left(\tan1^0.\tan89^0\right).\left(\tan2^0.\tan88^0\right).\left(\tan3^0.\tan87^0\right)...\tan45^0=\left(\tan1^0.\cot1^0\right).\left(\tan2^0.\cot2^0\right).\left(\tan3^0.\cot3^0\right)...1=1\)