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

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

Evaluate

$$\frac{25000000000000000000000000000000\sqrt{2}}{43301270189221934897939208206489}\approx 0.816496581$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\sin(45)}{2 \cdot 0.9659258262890683 ^ {2} - 1}$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{\frac{\sqrt{2}}{2}}{2\times 0.9659258262890683^{2}-1}$$

Calculate 0.9659258262890683 to the power of 2 and get 0.93301270189221934897939208206489.

$$\frac{\frac{\sqrt{2}}{2}}{2\times 0.93301270189221934897939208206489-1}$$

Multiply 2 and 0.93301270189221934897939208206489 to get 1.86602540378443869795878416412978.

$$\frac{\frac{\sqrt{2}}{2}}{1.86602540378443869795878416412978-1}$$

Subtract 1 from 1.86602540378443869795878416412978 to get 0.86602540378443869795878416412978.

$$\frac{\frac{\sqrt{2}}{2}}{0.86602540378443869795878416412978}$$

Express \frac{\frac{\sqrt{2}}{2}}{0.86602540378443869795878416412978} as a single fraction.

$$\frac{\sqrt{2}}{2\times 0.86602540378443869795878416412978}$$

Multiply 2 and 0.86602540378443869795878416412978 to get 1.73205080756887739591756832825956.

$$\frac{\sqrt{2}}{1.73205080756887739591756832825956}$$