Løs left(tan(25)right)^2-left(tan(15)right)^2/1-left(tan(25)right)^2left(tan(15)right)^2=

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

Evaluer

$$\frac{364115155823770524802496458866675000000000000000000000000000000}{2460970767646944749310490159796017021995186714703002124550619079}\approx 0,147955904$$

Løsningstrinn

Evaluate trigonometric functions in the problem

$$\frac{0,4663076581549986 ^ {2} - 0,2679491924311227 ^ {2}}{1 - 0,4663076581549986 ^ {2} 0,2679491924311227 ^ {2}}$$

Regn ut 0,4663076581549986 opphøyd i 2 og få 0,21744283205399903234258216600196.

$$\frac{0,21744283205399903234258216600196-0,2679491924311227^{2}}{1-0,4663076581549986^{2}\times 0,2679491924311227^{2}}$$

Regn ut 0,2679491924311227 opphøyd i 2 og få 0,07179676972449082242158358245529.

$$\frac{0,21744283205399903234258216600196-0,07179676972449082242158358245529}{1-0,4663076581549986^{2}\times 0,2679491924311227^{2}}$$

Trekk fra 0,07179676972449082242158358245529 fra 0,21744283205399903234258216600196 for å få 0,14564606232950820992099858354667.

$$\frac{0,14564606232950820992099858354667}{1-0,4663076581549986^{2}\times 0,2679491924311227^{2}}$$

Regn ut 0,4663076581549986 opphøyd i 2 og få 0,21744283205399903234258216600196.

$$\frac{0,14564606232950820992099858354667}{1-0,21744283205399903234258216600196\times 0,2679491924311227^{2}}$$

Regn ut 0,2679491924311227 opphøyd i 2 og få 0,07179676972449082242158358245529.

$$\frac{0,14564606232950820992099858354667}{1-0,21744283205399903234258216600196\times 0,07179676972449082242158358245529}$$

Multipliser 0,21744283205399903234258216600196 med 0,07179676972449082242158358245529 for å få 0,0156116929412221002758039360815931912019253141187991501797523684.

$$\frac{0,14564606232950820992099858354667}{1-0,0156116929412221002758039360815931912019253141187991501797523684}$$

Trekk fra 0,0156116929412221002758039360815931912019253141187991501797523684 fra 1 for å få 0,9843883070587778997241960639184068087980746858812008498202476316.

$$\frac{0,14564606232950820992099858354667}{0,9843883070587778997241960639184068087980746858812008498202476316}$$

Utvid \frac{0,14564606232950820992099858354667}{0,9843883070587778997241960639184068087980746858812008498202476316} ved å multiplisere både telleren og nevneren med 10000000000000000000000000000000000000000000000000000000000000000.

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

Forkort brøken \frac{1456460623295082099209985835466700000000000000000000000000000000}{9843883070587778997241960639184068087980746858812008498202476316} til minste felles nevner ved å dele teller og nevner på 4.

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