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Q.16

Expert-verified
Found in: Page 473

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Multiply and simplify: $\frac{\left(1+\mathrm{tan}\left(\theta \right)\right)\left(1+\mathrm{tan}\left(\theta \right)\right)-sec\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}$

on simplifying we get $2.$

See the step by step solution

## Step 1: Given information

We are given an expression $\frac{\left(1+\mathrm{tan}\left(\theta \right)\right)\left(1+\mathrm{tan}\left(\theta \right)\right)-sec\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}$

## Step 2: Multiply and simplify

We get,

$\frac{\left(1+\mathrm{tan}\left(\theta \right)\right)\left(1+\mathrm{tan}\left(\theta \right)\right)-sec\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=\frac{1+2\mathrm{tan}\left(\theta \right)+{\mathrm{tan}}^{2}\left(\theta \right)-se{c}^{2}\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=\frac{se{c}^{2}\left(\theta \right)+2\mathrm{tan}\left(\theta \right)-se{c}^{2}\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=\frac{2\mathrm{tan}\left(\theta \right)}{\mathrm{tan}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=2$

## Step 3: Conclusion

On simplifying we get the expression as $2.$