SOLUTION: if tan alpha = x + 1 and tan beta = x-1, show that 2cot(alpha- beta) = x^2

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Question 702592: if tan alpha = x + 1 and tan beta = x-1, show that 2cot(alpha- beta) = x^2
Answer by lwsshak3(11628) About Me  (Show Source):
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if tan alpha = x + 1 and tan beta = x-1, show that 2cot(alpha- beta) = x^2
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A=alpha=x+1
B=beta=x-1
..
2cot(A-B)=x^2
cot(A-B)=x^2/2
tan(A-B)=2/x^2
..
Identity: tan(A-B)
=(tanA-tanB)/(1+tanA*tanB)
=(x+1)-(x-1)/[1+(x+1)(x-1)]
=(x+1-x+1)/1+(x^2-1)=2/x^2
tan(A-B)=2/x^2
cot(A-B)=x^2/2
2cot(A-B)=x^2