求解 frac{sin^{2}48^{circ}}{cos^{2}42^{circ}}+frac{sec52^{circ}}{csc38^{circ}}-frac{tan^{2}40^{circ}}{cot^250^circ}+sin90^circcos0^circ

$$\frac { \sin ^ { 2 } 48 ^ { \circ } } { \cos ^ { 2 } 42 ^ { \circ } } + \frac { \sec 52 ^ { \circ } } { \csc 38 ^ { \circ } } - \frac { \tan ^ { 2 } 40 ^ { \circ } } { \cot ^ { 2 } 50 ^ { \circ } } + \sin 90 ^ { \circ } \cos 0 ^ { \circ }$$

求值

$$\frac{2870842171108398898530013049515629534691011490103339848511132534868303735795567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}\approx 2$$

求解步骤

对题中的三角函数求值

$$\frac{0.7431448254773941 ^ {2}}{0.7431448254773942 ^ {2}} + \frac{1.624269245482744}{1.6242692454827443} - \frac{0.8390996311772799 ^ {2}}{0.83909963117728 ^ {2}} + \sin(90) \cos(0)$$

计算 2 的 0.7431448254773941 乘方，得到 0.55226423163382653502897012671481。

$$\frac{0.55226423163382653502897012671481}{0.7431448254773942^{2}}+\frac{1.624269245482744}{1.6242692454827443}-\frac{0.8390996311772799^{2}}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

计算 2 的 0.7431448254773942 乘方，得到 0.55226423163382668365793522219364。

$$\frac{0.55226423163382653502897012671481}{0.55226423163382668365793522219364}+\frac{1.624269245482744}{1.6242692454827443}-\frac{0.8390996311772799^{2}}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

将分子和分母同时乘以 100000000000000000000000000000000 以展开 \frac{0.55226423163382653502897012671481}{0.55226423163382668365793522219364}。

$$\frac{55226423163382653502897012671481}{55226423163382668365793522219364}+\frac{1.624269245482744}{1.6242692454827443}-\frac{0.8390996311772799^{2}}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

将分子和分母同时乘以 10000000000000000 以展开 \frac{1.624269245482744}{1.6242692454827443}。

$$\frac{55226423163382653502897012671481}{55226423163382668365793522219364}+\frac{16242692454827440}{16242692454827443}-\frac{0.8390996311772799^{2}}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

\frac{55226423163382653502897012671481}{55226423163382668365793522219364} 与 \frac{16242692454827440}{16242692454827443} 相加，得到 \frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252}。

$$\frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252}-\frac{0.8390996311772799^{2}}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

计算 2 的 0.8390996311772799 乘方，得到 0.70408819104184715837886196294401。

$$\frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252}-\frac{0.70408819104184715837886196294401}{0.83909963117728^{2}}+\sin(90)\cos(0)$$

计算 2 的 0.83909963117728 乘方，得到 0.7040881910418473261987881984。

$$\frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252}-\frac{0.70408819104184715837886196294401}{0.7040881910418473261987881984}+\sin(90)\cos(0)$$

将分子和分母同时乘以 100000000000000000000000000000000 以展开 \frac{0.70408819104184715837886196294401}{0.7040881910418473261987881984}。

$$\frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252}-\frac{70408819104184715837886196294401}{70408819104184732619878819840000}+\sin(90)\cos(0)$$

将 \frac{1794051613645965980589349118007741600064748801243}{897025806822983193841037800335142264885013206252} 减去 \frac{70408819104184715837886196294401}{70408819104184732619878819840000}，得到 \frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}。

$$\frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}+\sin(90)\cos(0)$$

从三角函数值表中获取 \sin(90) 的值。

$$\frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}+1\cos(0)$$

从三角函数值表中获取 \cos(0) 的值。

$$\frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}+1\times 1$$

将 1 与 1 相乘，得到 1。

$$\frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}+1$$

\frac{1435421085554199294616851248464666196425972264351012763664496078997752153075567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000} 与 1 相加，得到 \frac{2870842171108398898530013049515629534691011490103339848511132534868303735795567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}。

$$\frac{2870842171108398898530013049515629534691011490103339848511132534868303735795567}{1435421085554199603913161801050963338265039225752327084846636455870551582720000}$$