Solve sin60^{circ}cos30^circ+cos60^circsin30^circ=sin90^circ

$$\sin 60 ^ { \circ } \cos 30 ^ { \circ } + \cos 60 ^ { \circ } \sin 30 ^ { \circ } = \sin 90 ^ { \circ }$$

Verify

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$\frac{\sqrt{3}}{2}\cos(30)+\cos(60)\sin(30)=\sin(90)$$

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

$$\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}+\cos(60)\sin(30)=\sin(90)$$

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

$$\left(\frac{\sqrt{3}}{2}\right)^{2}+\cos(60)\sin(30)=\sin(90)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\cos(60)\sin(30)=\sin(90)$$

Get the value of \cos(60) from trigonometric values table.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{1}{2}\sin(30)=\sin(90)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{1}{2}\times \frac{1}{2}=\sin(90)$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{1}{4}=\sin(90)$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}}{4}+\frac{1}{4}=\sin(90)$$

Since \frac{\left(\sqrt{3}\right)^{2}}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\left(\sqrt{3}\right)^{2}+1}{4}=\sin(90)$$

Get the value of \sin(90) from trigonometric values table.

$$\frac{\left(\sqrt{3}\right)^{2}+1}{4}=1$$

The square of \sqrt{3} is 3.

$$\frac{3+1}{4}=1$$

Add 3 and 1 to get 4.

$$\frac{4}{4}=1$$

Divide 4 by 4 to get 1.

$$1=1$$

Compare 1 and 1.

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