7) ABC is right-angled triangle at B, Prove that: $\sin^2 A + \sin^2 C = 1$
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$$ \text { If } \cos \mathrm{A}=\frac{2 \cos \mathrm{B}-1}{2-\cos \mathrm{B}} \text { prove that } \tan \frac{\mathrm{A}}{2}=\sqrt{3} \tan \frac{\mathrm{B}}{2} \cdot \text { Hence show that } \sin \mathrm{B}=\frac{\sqrt{3} \sin \mathrm{A}}{2+\cos \mathrm{A}} \text { . } $$
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