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Question Number 82879 by jagoll last updated on 25/Feb/20

$$\mathrm{prove}\mathrm{that}$$$$\frac{\cos {}^2\mathrm{a}+\sin {}^2\mathrm{b}}{\sin \mathrm{acos}\mathrm{a}+\sin \mathrm{bcos}\mathrm{b}}=\cot (\mathrm{a}+\mathrm{b})$$

Commented by mahdi last updated on 25/Feb/20

$$\mathrm{problem}:$$$$fora=0b=30\Rightarrow \frac{\cos {}^2\mathrm{a}+\sin {}^2\mathrm{b}}{\sin \mathrm{acos}\mathrm{a}+\sin \mathrm{bcos}\mathrm{b}}=\frac{1+0.25}{0+\frac{\sqrt{3}}{4}}=\frac{5\sqrt{3}}{3}$$$$andcot(0+30)=\sqrt{3}$$

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