다음을 풀어보세요: (frac{tan25^{circ}}{csc65^{circ}})^{2}+(frac{cot25^{circ}}{sec65^{circ}})^2+2tan18^circtan45^circtan72^circ

$$( \frac { \tan 25 ^ { \circ } } { \csc 65 ^ { \circ } } ) ^ { 2 } + ( \frac { \cot 25 ^ { \circ } } { \sec 65 ^ { \circ } } ) ^ { 2 } + 2 \tan 18 ^ { \circ } \tan 45 ^ { \circ } \tan 72 ^ { \circ }$$

계산

$$\frac{45442351761115914888034412436150224210730415685514322476705801937969715985475404991335325292689}{15147450587038641294478415595498206962310364838504310844441344450000000000000000000000000000000}\approx 3$$

해답 단계

Evaluate trigonometric functions in the problem

$${(\frac{0.4663076581549986}{1.1033779189624917})} ^ {2} + {(\frac{2.1445069205095586}{2.3662015831524985})} ^ {2} + 2 \cdot 0.3249196962329063 \tan(45) 3.0776835371752527$$

분자와 분모 모두에 10000000000000000을(를) 곱하여 \frac{0.4663076581549986}{1.1033779189624917}을(를) 확장합니다.

$$\left(\frac{4663076581549986}{11033779189624917}\right)^{2}+\left(\frac{2.1445069205095586}{2.3662015831524985}\right)^{2}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

3을(를) 추출 및 상쇄하여 분수 \frac{4663076581549986}{11033779189624917}을(를) 기약 분수로 약분합니다.

$$\left(\frac{1554358860516662}{3677926396541639}\right)^{2}+\left(\frac{2.1445069205095586}{2.3662015831524985}\right)^{2}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

\frac{1554358860516662}{3677926396541639}의 2제곱을 계산하여 \frac{2416031467266655914917579622244}{13527142578377765566699460806321}을(를) 구합니다.

$$\frac{2416031467266655914917579622244}{13527142578377765566699460806321}+\left(\frac{2.1445069205095586}{2.3662015831524985}\right)^{2}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

분자와 분모 모두에 10000000000000000을(를) 곱하여 \frac{2.1445069205095586}{2.3662015831524985}을(를) 확장합니다.

$$\frac{2416031467266655914917579622244}{13527142578377765566699460806321}+\left(\frac{21445069205095586}{23662015831524985}\right)^{2}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

\frac{21445069205095586}{23662015831524985}의 2제곱을 계산하여 \frac{459890993211339028795067396683396}{559890993211339027323350679250225}을(를) 구합니다.

$$\frac{2416031467266655914917579622244}{13527142578377765566699460806321}+\frac{459890993211339028795067396683396}{559890993211339027323350679250225}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

\frac{2416031467266655914917579622244}{13527142578377765566699460806321}과(와) \frac{459890993211339028795067396683396}{559890993211339027323350679250225}을(를) 더하여 \frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}을(를) 구합니다.

$$\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}+0.3249196962329063\times 2\times 3.0776835371752527\tan(45)$$

0.3249196962329063과(와) 2을(를) 곱하여 0.6498393924658126(을)를 구합니다.

$$\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}+0.6498393924658126\times 3.0776835371752527\tan(45)$$

0.6498393924658126과(와) 3.0776835371752527을(를) 곱하여 1.99999999999999938244315951584402(을)를 구합니다.

$$\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}+1.99999999999999938244315951584402\tan(45)$$

삼각법 값 표에서 \tan(45) 값을 가져옵니다.

$$\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}+1.99999999999999938244315951584402\times 1$$

1.99999999999999938244315951584402과(와) 1을(를) 곱하여 1.99999999999999938244315951584402(을)를 구합니다.

$$\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}+1.99999999999999938244315951584402$$

\frac{7573725293519320826744653583305434733489071583881254791964551016}{7573725293519320647239207797749103481155182419252155422220672225}과(와) 1.99999999999999938244315951584402을(를) 더하여 \frac{45442351761115914888034412436150224210730415685514322476705801937969715985475404991335325292689}{15147450587038641294478415595498206962310364838504310844441344450000000000000000000000000000000}을(를) 구합니다.

$$\frac{45442351761115914888034412436150224210730415685514322476705801937969715985475404991335325292689}{15147450587038641294478415595498206962310364838504310844441344450000000000000000000000000000000}$$