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Question Number 112542 by bobhans last updated on 08/Sep/20

$$\mathrm{If}7\sin \mathrm{y}=8\sin (\mathrm{y}+45°).\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\tan (\mathrm{y}+45°)?$$

Answered by bemath last updated on 08/Sep/20

$$\mathrm{let}\mathrm{x}=\mathrm{y}+45°;\mathrm{y}=\mathrm{x}-45°$$$$\iff 7\sin (\mathrm{x}-45°)=8\sin \mathrm{x}$$$$\iff 7(\frac{\sqrt{2}}{2}.\sin \mathrm{x}-\frac{\sqrt{2}}{2}.\cos \mathrm{x})=8\sin \mathrm{x}$$$$7\sqrt{2}\sin \mathrm{x}-7\sqrt{2}\cos \mathrm{x}=16\sin \mathrm{x}$$$$(7\sqrt{2}-16)\sin \mathrm{x}=7\sqrt{2}\cos \mathrm{x}$$$$\iff \tan \mathrm{x}=\frac{7\sqrt{2}}{7\sqrt{2}-16}$$$$\iff \tan (\mathrm{y}+45°)=\frac{7\sqrt{2}}{7\sqrt{2}-16}.$$

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