SOLUTION: What are the sequence of steps that verify the identity (cot x + cot y) / (cot x cot y -1) = (cos x sin y + sin x cos y) / (cos x cos y

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Question 678504: What are the sequence of steps that verify the identity (cot x + cot y) / (cot x cot y -1) = (cos x sin y + sin x cos y) / (cos x cos y - sin x sin y)
Answer by lwsshak3(11628) (Show Source):
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What are the sequence of steps that verify the identity
(cot x + cot y) / (cot x cot y -1) = (cos x sin y + sin x cos y) / (cos x cos y - sin x sin y)
start with left side:
(cot x + cot y) / (cot x cot y -1)
=(cos x/sin x+cos y/sin y)/(cos x/sin x*cos y/sin y-1
=[cos x sin y+sin x cosy/sin x sin y]/[(cos x cos y/sin x sin y)-1]
=[(cos x sin y+sin x cosy)/(sin x sin y)]/[(cos x cos y-sin x sin y)/(sin x sin y)]
(sin x sin y) denominators cancel out
=(cos x sin y+sin x cosy)/(cos x cos y-sin x sin y)
verified: left side=right side

SOLUTION: What are the sequence of steps that verify the identity (cot x + cot y) / (cot x cot y -1) = (cos x sin y + sin x cos y) / (cos x cos y - sin x sin y)