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Simplify the given expression

Simplify the given expression-example-1
User Gekkie
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By expressing the trigonometric functions in terms of sine and cosine, the simplified expression is 1 / (cos α * (cot β + tan α)).

How to simplify the expression

To simplify the expression (tan α + tan β) / (cot α + cot β), start by expressing the trigonometric functions in terms of sine and cosine:

tan α = sin α / cos α

tan β = sin β / cos β

cot α = cos α / sin α

cot β = cos β / sin β

Substitute these expressions into the original expression:

(tan α + tan β) / (cot α + cot β) = (sin α / cos α + sin β / cos β) / (cos α / sin α + cos β / sin β)

Find a common denominator for the numerators and denominators:

[(sin α * sin β) / (cos α * cos β)] / [(cos α * sin β + cos β * sin α) / (sin α * sin β)]

Simplify further by canceling out sin α * sin β:

1 / [(cos α * cos β) / (cos α * sin β + cos β * sin α)]

Now, simplify the denominator by factoring out a common factor of cos α:

1 / [cos α * (cos β / sin β + sin α)]

Finally, rewrite the expression as:

1 / (cos α * (cot β + tan α))

Therefore, the simplified expression is 1 / (cos α * (cot β + tan α)).

User Andy Braham
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