Toán Lớp 9: tính
Tan25 . tan 65 + 2 Sin ²30 + 2Sin ²60
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Toán Lớp 9: tính
Tan25 . tan 65 + 2 Sin ²30 + 2Sin ²60
Comments ( 1 )
\tan \left( {{{90}^o} – \alpha } \right) = \cot \alpha ,\sin \left( {{{90}^o} – \alpha } \right) = \cos \alpha \Rightarrow {\sin ^2}\left( {{{90}^o} – \alpha } \right) = {\cos ^2}\alpha \\
\tan {25^o}.\tan {65^o} + 2{\sin ^2}{30^o} + 2{\sin ^2}{60^o}\\
= \tan {25^o}.\cot {25^o} + 2\left( {{{\sin }^2}{{30}^o} + {{\sin }^2}{{60}^o}} \right)\\
= 1 + 2\left( {{{\sin }^2}{{30}^o} + {{\cos }^2}{{30}^o}} \right) = 1 + 2 = 3
\end{array}$