Solve 1-2sin(30^circ)+frac{{left(cos(30^circ)right)}^2}{2}

$$1-2 \sin ( 30 ^ { \circ } ) + \frac{ { \left( \cos ( 30 ^ { \circ } ) \right) }^{ 2 } }{ 2 }$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

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

$$1-2\times \frac{1}{2}+\frac{\left(\cos(30)\right)^{2}}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$1-1+\frac{\left(\cos(30)\right)^{2}}{2}$$

Subtract 1 from 1 to get 0.

$$0+\frac{\left(\cos(30)\right)^{2}}{2}$$

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

$$0+\frac{\left(\frac{\sqrt{3}}{2}\right)^{2}}{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$0+\frac{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}}{2}$$

Express \frac{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}}{2} as a single fraction.

$$0+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}\times 2}$$

The square of \sqrt{3} is 3.

$$0+\frac{3}{2^{2}\times 2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$0+\frac{3}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$0+\frac{3}{8}$$

Add 0 and \frac{3}{8} to get \frac{3}{8}.

$$\frac{3}{8}$$