Question

Find the value of sin 15( degree )

Answer 1

sin30=1/2
sin30/2=sin15
1/2/2=sin15
1/4=sin15

Answer 2

$\bold{\huge{\underline{Solution-}}}$

$\bf \: Used \: formula- \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{1. \bf \: sin(A - B) = sinA \: cosB - \: \: cosA \: sinB }$

$\bf \: sin \: 15 \degree \: = sin \: (45 \degree \: -30 \degree) \: \\ \\ \boxed{\because \: 15\degree = 45 \degree - 30 \degree} \: \\ \\ \bf \: now \: using \: the \: sin(A - B) \:where \: A = 45 \degree \: B = 30 \degree \: \\ \\ \implies \bf \: sin \:45 \degree cos \: 30\degree - cos \: 45 \degree \: sin \: 30 \degree \: \\ \\ \implies \bf \: \frac{1}{ \sqrt{2} } . \frac{ \sqrt{3} }{2} - \frac{1}{ \sqrt{2} } . \frac{1}{2} \\ \\ \implies \bf \: \frac{ \sqrt{3} }{ \sqrt[2]{2} } - \frac{1}{ \sqrt[2]{2} } \\ \\ \implies \bf \: \frac{ \sqrt{3} - 1 }{ \sqrt[2]{2} }$