Question

If sin(A+B) = sin A cos B + cos A sin B, then the value of sin 75degree is what ???

Answer 1

Let A=30° and B = 45°

$sin(30^{0}+45^{0})$

$=sin(75^{0})$

$=sin30^{0}cos45^{0}+cos30^{0}sin45^{0}$

$=\frac{1}{2} (\frac{1}{ \sqrt{2} }) + \frac{ \sqrt{3} }{2} (\frac{1}{ \sqrt{2} })$

$=\frac{1}{\sqrt{2} } ( \frac{ \sqrt{3} + 1}{2} )$