Using Sum and Difference identities, verify \[ \frac{\sin (x+y)}{\cos (x-y)}=\frac{\cot x+\cot y}{1+\cot x \cot y} \]
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Step 1: Start by expressing the left-hand side (LHS) of the equation using the sum and difference identities for sine and cosine: \[ \sin(x+y) = \sin x \cos y + \cos x \sin y \] \[ \cos(x-y) = \cos x \cos y + \sin x \sin y \] Thus, the LHS becomes: \[ Show more…
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