Solve sin^230sin20/sin40sin50sin10

$$\frac { \sin ^ { 2 } 30 \sin 20 } { \sin 40 \sin 50 \sin 10 }$$

Evaluate

$$\frac{42752517915708587500000000000000000000000000000}{42752517915708583273808906505812727229627178841}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\sin^{2}(30) 0.3420201433256687}{0.6427876096865393 \cdot 0.766044443118978 \cdot 0.17364817766693033}$$

Get the value of \sin(30) from trigonometric values table.

$$\frac{0.3420201433256687\times \left(\frac{1}{2}\right)^{2}}{0.6427876096865393\times 0.766044443118978\times 0.17364817766693033}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{0.3420201433256687\times \frac{1}{4}}{0.6427876096865393\times 0.766044443118978\times 0.17364817766693033}$$

Multiply 0.3420201433256687 and \frac{1}{4} to get \frac{3420201433256687}{40000000000000000}.

$$\frac{\frac{3420201433256687}{40000000000000000}}{0.6427876096865393\times 0.766044443118978\times 0.17364817766693033}$$

Multiply 0.6427876096865393 and 0.766044443118978 to get 0.4924038765061039868913949728354.

$$\frac{\frac{3420201433256687}{40000000000000000}}{0.4924038765061039868913949728354\times 0.17364817766693033}$$

Multiply 0.4924038765061039868913949728354 and 0.17364817766693033 to get 0.085505035831417166547617813011625454459254357682.

$$\frac{\frac{3420201433256687}{40000000000000000}}{0.085505035831417166547617813011625454459254357682}$$

Express \frac{\frac{3420201433256687}{40000000000000000}}{0.085505035831417166547617813011625454459254357682} as a single fraction.

$$\frac{3420201433256687}{40000000000000000\times 0.085505035831417166547617813011625454459254357682}$$

Multiply 40000000000000000 and 0.085505035831417166547617813011625454459254357682 to get 3420201433256686.66190471252046501817837017430728.

$$\frac{3420201433256687}{3420201433256686.66190471252046501817837017430728}$$

Expand \frac{3420201433256687}{3420201433256686.66190471252046501817837017430728} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{342020143325668700000000000000000000000000000000}{342020143325668666190471252046501817837017430728}$$

Reduce the fraction \frac{342020143325668700000000000000000000000000000000}{342020143325668666190471252046501817837017430728} to lowest terms by extracting and canceling out 8.

$$\frac{42752517915708587500000000000000000000000000000}{42752517915708583273808906505812727229627178841}$$