Question

Write the expression as the sine, cosine, or tangent of an angle.

sin 48° cos 15° - cos 48° sin 15°

Answer 1

`\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ \boxed{sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})}`


`\bf cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\ -------------------------------\\\\ sin(48^o)cos(15^o)-cos(48^o)sin(15^o)\implies sin(48^o+15^o) \\\\\\ sin(63^o)`

Answer 2

The expression in terms of the sine expression is given by:

`\sin 48\cos 15-\cos 48\sin 15=\sin 33\degree`

Explanation:

The expression is given as:

`\sin 48\cos 15-\cos 48\sin 15`

Now we know that the formula is as follows:

`\sin \alpha \cos \beta-\cos \alpha \sin \beta=\sin (\alpha-\beta)`

Here on comparing the given expression with the above formula we have:

`\sin 48\cos 15-\cos 48\sin 15=\sin (48-15)`

i.e.

`\sin 48\cos 15-\cos 48\sin 15=\sin 33`