Question

please answer 3rd question in steps

Answer 1

A =45 °

B = 30°

Sin A = Sin 45°

=1/√2

Cos A = cos 45°

=1/√2

Sin B = sin 30°

=1/2

$\frac{sin \: a \: }{cos \: a + sin \: a \: sin \: b}$

$= \frac{ \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } \times \frac{1}{2} }$

$= \frac{ \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } + \frac{1}{2 \sqrt{2} } }$

$= \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2 + 1}{2 \sqrt{2} } }$

$= \frac{ \frac{1}{ \sqrt{2} } }{ \frac{3}{2 \sqrt{2} } }$

$= \frac{1 \times 2 \sqrt{2} }{3 \times \sqrt{2} }$

$= \frac{2}{3}$

Hence verified ✔