Question

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

sin 52° cos 13° - cos 52° sin 13°

Answer 1

`\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)`

Answer 2

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 )`