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If $sin eta=frac{1}{5} sin (2 alpha+eta)$, then prove that $an (alpha+eta)=frac{3}{2} an alpha$...

Question

If $sin eta=frac{1}{5} sin (2 alpha+eta)$, then prove that $an (alpha+eta)=frac{3}{2} an alpha$

If $sin eta=frac{1}{5} sin (2 alpha+eta)$, then prove that $ an (alpha+eta)=frac{3}{2} an alpha$



Answers

Prove the identity. $$\sin (\alpha+\beta) \sin (\alpha-\beta)=\sin ^{2} \alpha-\sin ^{2} \beta$$


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