Ratkaise sin(45)/2left(cos(15)right)^2-1

$$\frac{ \sin ( 45 ) }{ 2 { \left( \cos ( 15 ) \right) }^{ 2 } -1 }$$

Laske

$$\frac{25000000000000000000000000000000\sqrt{2}}{43301270189221934897939208206489}\approx 0,816496581$$

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

$$\frac{\sin(45)}{2 \cdot 0,9659258262890683 ^ {2} - 1}$$

Hae kaavan \sin(45) arvo trigonometristen arvojen taulukosta.

$$\frac{\frac{\sqrt{2}}{2}}{2\times 0,9659258262890683^{2}-1}$$

Laske 0,9659258262890683 potenssiin 2, jolloin ratkaisuksi tulee 0,93301270189221934897939208206489.

$$\frac{\frac{\sqrt{2}}{2}}{2\times 0,93301270189221934897939208206489-1}$$

Kerro 2 ja 0,93301270189221934897939208206489, niin saadaan 1,86602540378443869795878416412978.

$$\frac{\frac{\sqrt{2}}{2}}{1,86602540378443869795878416412978-1}$$

Vähennä 1 luvusta 1,86602540378443869795878416412978 saadaksesi tuloksen 0,86602540378443869795878416412978.

$$\frac{\frac{\sqrt{2}}{2}}{0,86602540378443869795878416412978}$$

Ilmaise \frac{\frac{\sqrt{2}}{2}}{0,86602540378443869795878416412978} säännöllisenä murtolukuna.

$$\frac{\sqrt{2}}{2\times 0,86602540378443869795878416412978}$$

Kerro 2 ja 0,86602540378443869795878416412978, niin saadaan 1,73205080756887739591756832825956.

$$\frac{\sqrt{2}}{1,73205080756887739591756832825956}$$