12/ sin 43°+sin 133°

[latex] \frac{12}{sin43+sin133} = \frac{12}{2sin88\cdot cos45}= \frac{6}{sin(90-2)\cdot \frac{\sqrt2}{2}} = \frac{6\cdot 2}{\sqrt2\cdot cos2} = \frac{6\sqrt2}{cos2} [/latex] [latex] \frac{12}{sin^243+sin^2133} = \frac{12}{sin^243+sin^2(90+43)} = \frac{12}{sin^243+cos^243}=\frac{12}{1}=12 [/latex]