Question

Use identities (no calculators) to find the exact value for (sin 15)(cos 45) + (cos 15)(sin 45).

Answer 1

This is the 'addition angle formula
\[sin(a+b)=sin(a)cos(b)+cos(a)sin(b)\]

Answer 2

here
\[a=15, b=45\] so the left hand side is
\[sin(15+45)=sin(60)\]

Answer 3

\[sin(60)=\frac{\sqrt{3}}{2}\]

Answer 4

Thanks! What if they are angles such as
Use identities (no calculators) to find the exact value for (sin 38)(sin 112) -( cos 38)(cos 112)

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