Question

What is sin 20° cos 4° + cos 20° sin 4° equal to?

cos 16°
sin 16°
cos 24°
sin 24°

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) \\\\ -------------------------------\\\\ sin(20^o)cos(4^o)+cos(20^o)sin(4^o)\implies sin(20^o+4^o)\implies sin(24^o)`

Answer 2

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

So we know this identity:


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

Given that α = 20° and β = 4°, the solution is:


`sin(24)`