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Q. 71

Expert-verifiedFound in: Page 475

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Establish each identity.

$sec\theta -\mathrm{cos}\theta =\mathrm{sin}\theta \mathrm{tan}\theta $

The left side of the given equation has been simplified to give the right side.

The given equation is $sec\theta -\mathrm{cos}\theta =\mathrm{sin}\theta \mathrm{tan}\theta $

Consider the left side of the given equation and simplify.

$sec\theta -\mathrm{cos}\theta =\frac{1}{\mathrm{cos}\theta}-\mathrm{cos}\theta \phantom{\rule{0ex}{0ex}}=\frac{1-{\mathrm{cos}}^{2}\theta}{\mathrm{cos}\theta}\phantom{\rule{0ex}{0ex}}=\frac{{\mathrm{sin}}^{2}\theta}{\mathrm{cos}\theta}\phantom{\rule{0ex}{0ex}}=\mathrm{sin}\theta \frac{\mathrm{sin}\theta}{\mathrm{cos}\theta}\phantom{\rule{0ex}{0ex}}=\mathrm{sin}\theta \mathrm{tan}\theta $

Thus, the given identity is established.

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