Question 6.6.5.6: Establishing an Identity establishing the identity: cos(α-β)......
Establishing an Identity
Establishing the identity: {\frac{\cos\left(\alpha-\beta\right)}{\sin\alpha\sin\beta}}=\cot\alpha\cot\beta+1
{\frac{\cos\left(\alpha-\beta\right)}{\sin\alpha\sin\beta}}={\frac{\cos\alpha\cos\beta+\sin\alpha\sin\beta}{\sin\alpha\sin\beta}}
={\frac{\cos\alpha\cos\beta}{\sin\alpha\sin\beta}}+{\frac{\sin\alpha\sin\beta}{\sin\alpha\sin\beta}}
={\frac{\cos\alpha}{\sin\alpha}}\cdot{\frac{\cos\beta}{\sin\beta}}+1
=\cot\alpha\cot\beta+1
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