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Question Number 83811 by Power last updated on 06/Mar/20

Commented by Power last updated on 06/Mar/20

$$\mathrm{thanks}$$

Commented by john santu last updated on 06/Mar/20

$$\sin (41+\mathrm{x})=\sin (\mathrm{x}+19)+\sin (\mathrm{x}-19)$$$$\Rightarrow \sin (41+\mathrm{x})-\sin (\mathrm{x}-19)=\sin (\mathrm{x}+19)$$$$2\cos (\mathrm{x}+11)\sin 30=\sin (\mathrm{x}+19)$$$$\cos (\mathrm{x}+11)=\sin (\mathrm{x}+19)$$$$\cos (\mathrm{x}+11)=\cos (90-\mathrm{x}-19)$$$$\Rightarrow \mathrm{x}+11=71-\mathrm{x}+2\mathrm{k}\pi$$$$2\mathrm{x}=60+2\mathrm{k}\pi \Rightarrow \mathrm{x}=30+\mathrm{k}\pi$$$$$$

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