Question

Evaluating an Expression

Evaluate the expression without using a calculator

${\left(sin{60}^{°}\right)}^{\mathbf{2}}\mathbf{+}{\left(cos{60}^{°}\right)}^{\mathbf{2}}$

Short answer

The answer of the expression is 1.

Step-by-step solution

Step 1. Given information

A trigonometric expression is given as ${\left(\sin {60}^{°}\right)}^2+{\left(\cos {60}^{°}\right)}^2$.

Step 2. Concept used

To simplify the problem, use trigonometric ratios. Replace the ratio values in the expression and do the calculation. For more simplification, utilize trigonometric identities.

Step 3. Calculation

The given expression is ${\left(\sin {60}^{°}\right)}^2+{\left(\cos {60}^{°}\right)}^2$, substitute the values as-

$\begin{array}{l}\because \sin {60}^{°}=\frac{\sqrt{3}}{2}\&\cos {60}^{°}=\frac{1}{2}\\ ={\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2\\ =\frac{3}{4}+\frac{1}{4}\\ =\frac{4}{4}\\ =1\end{array}$