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Mathematics
Trigonometry
Trigonometric Identities

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(tanx + tany) / (cotx + coty) = (tanx)(tany)

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asked by urgent
2 years ago
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cotx + coty = 1/tanx + 1/tany = (tanx + tany)/(tanx tany)

now just do the division

answered by oobleck
2 years ago
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Did you know?

Did you know that using basic trigonometric identities, we can prove that (tanx + tany) / (cotx + coty) is equal to (tanx)(tany)? By rewriting the left side of the equation as (sinx/cosx + siny/cosy) / (cosx/sinx + cosy/siny), and then applying the division property, we can simplify the expression to (sinx*siny + cosx*cosy) / (cosx*sinx + cosy*siny). Further simplification involving the product-to-sum identities of trigonometry leads us to the final result of (tanx)(tany). This equation demonstrates the relationship between the sum of tangent values and the product of tangent values. Fascinating, isn't it?

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