Question

Find the value of sin 75°

Answer 1

sin ( A+B ) = sin A * cos B + cos A * sin B
sin ( 30+45 ) = sin 30 cos 45 + cos 30 * sin 45
sin 75 = (1/2)*(1/√2) + (√3/2)*(1/√2)
sin 75 =( 1/2√2 )+ (√3/2√2)
sin 75 = (1+√3)/2√2

Answer 2

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

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

$\bf \: sin \: 75 \degree \: = sin \: (45 \degree \: + 30 \degree) \: \\ \\ \boxed{\because \: 75\degree = 45 \degree + 30 \degree} \: \\ \\ \bf \: now \: using \: the \: sin(A + B) \:where \: A = 45 \degree \: B = 30 \degree \: \\ \\ \implies \bf \: sin \:45 \degree cos \: 30\degree + cos \: 45 \degree \: sin \: 30 \degree \: \\ \\ \implies \bf \: \frac{1}{ \sqrt{2} } . \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } . \frac{1}{2} \\ \\ \implies \bf \: \frac{ \sqrt{3} }{ \sqrt[2]{2} } + \frac{1}{ \sqrt[2]{2} } \\ \\ \implies \bf \: \frac{ \sqrt{3} + 1 }{ \sqrt[2]{2} }$