{1 + \tan \alpha \tan \beta }(1+ \tan \alpha \tan \beta \neq 0)利用这些公式可以将一些不是特殊角的三角函数转化为特殊角的三角函数来求值.如:\tan 105^{{\circ} }= \tan (45^{{\circ} }+ 60^{{\circ} })= \dfrac{\tan 45^{{\circ} } + \tan 60^{{\circ} }}{1 - \ta...
关于三角函数有如下的公式:\sin (\alpha + \beta )=\sin \alpha \cos \beta + \cos \alpha \sin \beta ①\cos (\alpha + \beta )=\cos \alpha \cos \beta -\sin \alpha \sin \beta ②\tan (\alpha + \beta ) = \dfrac{\tan \alpha + \tan \beta }{1 - \tan \alpha \ast \ta...
关于三角函数有如下公式:$$ \sin ( \alpha + \beta ) = \sin \alpha \cos \beta + \cos \alpha \sin \beta $$,$$ \sin ( \alpha - \beta ) = \sin \alpha \cos \beta - \cos \alpha \sin \beta ; $$$ \cos ( \alpha + \beta ) = \cos \alpha \cos \beta - \sin \alpha...
3. (1)$$ \frac { 1 } { 2 } \left[ \sin ( \alpha + \beta ) + \sin ( \alpha - \beta ) \right] $$ (2)$$ \frac { 1 } { 2 } \left[ \sin ( \alpha + \beta ) - \sin ( \alpha - \beta ) \right] $$ (3)$$ \frac { 1 } { 2 } \left[ \co...
cos \alpha \cos \beta + \sin \alpha \sin \beta $$$ \tan ( \alpha + \beta ) = \frac { \tan \alpha + \tan \beta } { 1 - \tan \alpha \tan \beta } ; $$$ \tan ( \alpha - \beta ) = \frac { \tan \alpha - \tan \beta } { 1 + \tan \alpha \tan \be...
两角和与差的三角函数公式$$ \sin ( \alpha + \beta ) = \sin \alpha \cos \beta + \cos \alpha \sin \beta $$($$ S _ { \alpha + \beta } $$)$$ \sin ( \alpha - \beta ) = \textcircled { 1 } \_ \_ \_ ; $$( $$ S _ { \alpha - \beta } $$)$$ \cos ( \...
9.(1)积化和差公式:$$ \sin \alpha \cos \beta = \frac { 1 } { 2 } \left[ \sin ( \alpha + \beta ) + \sin ( \alpha - \beta ) \right] ; $$$ \cos \alpha \sin \beta = \frac { 1 } { 2 } \left[ \sin ( \alpha + \beta ) - \sin ( \alpha - \be...
2.两角差的正弦、余弦、正切公式 (1)$$ ) \sin \alpha \cos \beta - \cos \alpha \sin \beta = \sin ( \alpha - \beta ) $$ (2)$$ \cos \alpha \cos \beta + \sin \alpha \sin \beta = \cos ( \alpha - \beta ) . $$ (3)$$ \frac { \tan \alpha - \tan \beta } {...
两角和与差的余弦公式$$ \cos ( \alpha - \beta ) = \cos \alpha \cos \alpha + \sin \alpha \sin \beta $$$ \cos ( \alpha + \beta ) = \underline { \cos \alpha \cos \beta - \sin \alpha \sin \beta } $$问题如何快速记忆两角和与差的余弦公式?两角和与差的余弦公式的结构特...
证明下列积化和差公式: (1)\sin\alpha \cos\beta =\frac{1}{2} [\sin(\alpha +\beta )+\sin(\alpha -\beta )] (2)\cos\alpha \sin\beta =\frac{1}{2} [\sin(\alpha +\beta )-\sin(\alpha -\beta )] (3)\cos\alpha \cos\beta =\frac{1}{2}[\cos(\alpha +\beta )+\c...