aminat75u

2023-03-14

How to use the fundamental identities to simplify $\mathrm{sin}\beta \mathrm{tan}\beta +\mathrm{cos}\beta$?

Dillan Perez

Beginner2023-03-15Added 6 answers

$f\left(b\right)=\mathrm{sin}b.\mathrm{tan}b+\mathrm{cos}b=\left(\mathrm{sin}b\right)\frac{\mathrm{sin}b}{\mathrm{cos}b}+\mathrm{cos}b=$

$=\frac{{\mathrm{sin}}^{2}b+{\mathrm{cos}}^{2}b}{\mathrm{cos}b}=\frac{1}{\mathrm{cos}b}=\mathrm{sec}b$

$=\frac{{\mathrm{sin}}^{2}b+{\mathrm{cos}}^{2}b}{\mathrm{cos}b}=\frac{1}{\mathrm{cos}b}=\mathrm{sec}b$