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Write the expression as either the sine, cosine, or tangent of a single angle.

sin 52° cos 13° - cos 52° sin 13°

2 Answers

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\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(52^o)cos(13^o)-cos(52^o)sin(13^o)\implies sin(52^o-13^o)\implies sin(39^o)

User Ali Shahzad
by
7.2k points
5 votes

Answer:
sin\left ( 39\right )

Explanation:


sin\left ( a+b\right )=sinacosb+cosasinb


sin\left ( a-b\right )=sinacosb-cosasinb

Using above formula


sin\left ( 52-13\right )=sin52cos13-cos52sin13


sin\left ( 39\right )

User Ruslan Plastun
by
6.8k points