Question

12/ sin 43°+sin 133°

Answer 1

$frac{12}{sin43+sin133} = frac{12}{2sin88cdot cos45}= frac{6}{sin(90-2)cdot frac{sqrt2}{2}} = frac{6cdot 2}{sqrt2cdot cos2} = frac{6sqrt2}{cos2}$


$frac{12}{sin^243+sin^2133} = frac{12}{sin^243+sin^2(90+43)} = frac{12}{sin^243+cos^243}=frac{12}{1}=12$