Rui Baldwin

2021-02-21

Multiply and simplify:
$\frac{(\mathrm{sin}\theta +\mathrm{cos}\theta )(\mathrm{sin}\theta +\mathrm{cos}\theta )-1}{\mathrm{sin}\theta \mathrm{cos}\theta}$

Liyana Mansell

Skilled2021-02-22Added 97 answers

Use the square of a binomal:

$(a+b{)}^{2}=(a+b)(a+b)={a}^{2}+2ab+{b}^{2}$

$=\frac{({\mathrm{sin}}^{2}\theta +2\mathrm{sin}\mathrm{cos}\theta +{\mathrm{cos}}^{2}\theta )-1}{\mathrm{sin}\theta \mathrm{cos}\theta}$

$=\frac{(2\mathrm{sin}\theta \mathrm{cos}\theta +{\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta )-1}{\mathrm{sin}\theta \mathrm{cos}\theta}$

Use the Pythagorean identity:${\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta =1$

$=\frac{(2\mathrm{sin}\theta \mathrm{cos}\theta +1)-1}{\mathrm{sin}\theta \mathrm{cos}\theta}$

Simplify:

$\frac{2\mathrm{sin}\theta \mathrm{cos}\theta}{\mathrm{sin}\theta \mathrm{cos}\theta}=2$

Use the Pythagorean identity:

Simplify:

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