Solve sin^{2}30^{circ}+cos^260^circ+sin30^circcos60^circ=3/4

$$\sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 60 ^ { \circ } + \sin 30 ^ { \circ } \cos 60 ^ { \circ } = \frac { 3 } { 4 }$$

Verify

Solution Steps

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

$$\left(\frac{1}{2}\right)^{2}+\left(\cos(60)\right)^{2}+\sin(30)\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{4}+\left(\cos(60)\right)^{2}+\sin(30)\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{4}+\left(\frac{1}{2}\right)^{2}+\sin(30)\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{4}+\frac{1}{4}+\sin(30)\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{2}+\sin(30)\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{2}+\frac{1}{2}\cos(60)=\frac{3}{4}$$

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

$$\frac{1}{2}+\frac{1}{2}\times \frac{1}{2}=\frac{3}{4}$$

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

$$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$$

Add \frac{1}{2} and \frac{1}{4} to get \frac{3}{4}.

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

Compare \frac{3}{4} and \frac{3}{4}.

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