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Q32.

Expert-verifiedFound in: Page 488

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Evaluating an Expression**

**Evaluate the expression without using a calculator**

**${\left(sin{60}^{\xb0}\right)}^{\mathbf{2}}\mathbf{+}{\left(cos{60}^{\xb0}\right)}^{\mathbf{2}}$**

The answer of the expression is **1**.

A trigonometric expression is given as ${\left(\mathrm{sin}{60}^{\xb0}\right)}^{2}+{\left(\mathrm{cos}{60}^{\xb0}\right)}^{2}$.

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

The given expression is ${\left(\mathrm{sin}{60}^{\xb0}\right)}^{2}+{\left(\mathrm{cos}{60}^{\xb0}\right)}^{2}$, substitute the values as-

$\begin{array}{l}\because \mathrm{sin}{60}^{\xb0}=\frac{\sqrt{3}}{2}\&\mathrm{cos}{60}^{\xb0}=\frac{1}{2}\\ ={\left(\frac{\sqrt{3}}{2}\right)}^{2}+{\left(\frac{1}{2}\right)}^{2}\\ =\frac{3}{4}+\frac{1}{4}\\ =\frac{4}{4}\\ =1\end{array}$

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