다음을 풀어보세요: left(tan(25)right)^2-left(tan(15)right)^2/1-left(tan(25)right)^2left(tan(15)right)^2=

$$\frac{ { \left( \tan ( 25 ) \right) }^{ 2 } - { \left( \tan ( 15 ) \right) }^{ 2 } }{ 1- { \left( \tan ( 25 ) \right) }^{ 2 } { \left( \tan ( 15 ) \right) }^{ 2 } } =$$

계산

$$\frac{364115155823770524802496458866675000000000000000000000000000000}{2460970767646944749310490159796017021995186714703002124550619079}\approx 0.147955904$$

해답 단계

Evaluate trigonometric functions in the problem

$$\frac{0.4663076581549986 ^ {2} - 0.2679491924311227 ^ {2}}{1 - 0.4663076581549986 ^ {2} 0.2679491924311227 ^ {2}}$$

0.4663076581549986의 2제곱을 계산하여 0.21744283205399903234258216600196을(를) 구합니다.

$$\frac{0.21744283205399903234258216600196-0.2679491924311227^{2}}{1-0.4663076581549986^{2}\times 0.2679491924311227^{2}}$$

0.2679491924311227의 2제곱을 계산하여 0.07179676972449082242158358245529을(를) 구합니다.

$$\frac{0.21744283205399903234258216600196-0.07179676972449082242158358245529}{1-0.4663076581549986^{2}\times 0.2679491924311227^{2}}$$

0.21744283205399903234258216600196에서 0.07179676972449082242158358245529을(를) 빼고 0.14564606232950820992099858354667을(를) 구합니다.

$$\frac{0.14564606232950820992099858354667}{1-0.4663076581549986^{2}\times 0.2679491924311227^{2}}$$

0.4663076581549986의 2제곱을 계산하여 0.21744283205399903234258216600196을(를) 구합니다.

$$\frac{0.14564606232950820992099858354667}{1-0.21744283205399903234258216600196\times 0.2679491924311227^{2}}$$

0.2679491924311227의 2제곱을 계산하여 0.07179676972449082242158358245529을(를) 구합니다.

$$\frac{0.14564606232950820992099858354667}{1-0.21744283205399903234258216600196\times 0.07179676972449082242158358245529}$$

0.21744283205399903234258216600196과(와) 0.07179676972449082242158358245529을(를) 곱하여 0.0156116929412221002758039360815931912019253141187991501797523684(을)를 구합니다.

$$\frac{0.14564606232950820992099858354667}{1-0.0156116929412221002758039360815931912019253141187991501797523684}$$

1에서 0.0156116929412221002758039360815931912019253141187991501797523684을(를) 빼고 0.9843883070587778997241960639184068087980746858812008498202476316을(를) 구합니다.

$$\frac{0.14564606232950820992099858354667}{0.9843883070587778997241960639184068087980746858812008498202476316}$$

분자와 분모 모두에 10000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 \frac{0.14564606232950820992099858354667}{0.9843883070587778997241960639184068087980746858812008498202476316}을(를) 확장합니다.

$$\frac{1456460623295082099209985835466700000000000000000000000000000000}{9843883070587778997241960639184068087980746858812008498202476316}$$

4을(를) 추출 및 상쇄하여 분수 \frac{1456460623295082099209985835466700000000000000000000000000000000}{9843883070587778997241960639184068087980746858812008498202476316}을(를) 기약 분수로 약분합니다.

$$\frac{364115155823770524802496458866675000000000000000000000000000000}{2460970767646944749310490159796017021995186714703002124550619079}$$