Question

Simplify: (sin 42°) cos 38° - (cos 42°) sin 38° SHOW WORK WILL MARK BRAINLIEST

Answer 1

Answer:

$\large\boxed{(\sin42^o)(\cos38^o)-(\cos42^o)(\sin38^o)=\sin4^o}$

Step-by-step explanation:

$(\sin42^o)(\cos38^o)-(\cos42^o)(\sin38^o)\\\\\text{use}\ \sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta\\\\\underbrace{(\sin42^o)}_{\sin\alpha}\underbrace{(\cos38^o)}_{\cos\beta}-\underbrace{(\cos42^o)}_{\cos\alpha}\underbrace{(\sin38^o)}_{\sin\beta}\\\\=\underbrace{\sin(42^o-38^o)}_{\sin(\alpha-\beta)}=\sin4^o$