# How do you find the exact value of the expression by using appropriate identities sin(79)cos(49)-cos(79)sin(49)

Hana Buck 2022-09-18 Answered
How do you find the exact value of the expression by using appropriate identities $\mathrm{sin}\left(79\right)\mathrm{cos}\left(49\right)-\mathrm{cos}\left(79\right)\mathrm{sin}\left(49\right)$?
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Abdiel Nelson
Using the identity
$\mathrm{sin}\left(\alpha -\beta \right)=\mathrm{sin}\left(\alpha \right)\mathrm{cos}\left(\beta \right)-\mathrm{cos}\left(\alpha \right)\mathrm{sin}\left(\beta \right)$
$\mathrm{sin}\left({79}^{\circ }\right)\mathrm{cos}\left({49}^{\circ }\right)-\mathrm{cos}\left({79}^{\circ }\right)\mathrm{sin}\left({49}^{\circ }\right)=\mathrm{sin}\left({79}^{\circ }-{49}^{\circ }\right)$
$=\mathrm{sin}\left({30}^{\circ }\right)$
$=\frac{1}{2}$

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