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Q30.

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**

**$\mathit{s}\mathit{i}\mathit{n}{\mathbf{30}}^{\mathbf{\xb0}}\mathit{c}\mathit{s}\mathit{c}{\mathbf{30}}^{\mathbf{\xb0}}$**

The answer of the expression is **1**

A trigonometric expression is given as $\mathrm{sin}{30}^{\xb0}\mathrm{csc}{30}^{\xb0}$.

Use trigonometric ratios to simplify the equation. Replace the values of the ratios in the expression and do the computation.

The given expression is $\mathrm{sin}{30}^{\xb0}\mathrm{csc}{30}^{\xb0}$, substitute the values as-

$\begin{array}{l}\because \mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta}\\ =\mathrm{sin}{30}^{\xb0}\times \frac{1}{\mathrm{sin}{30}^{\xb0}}\\ =1\end{array}$

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