289731JmG 289731JmG

25-07-2017
Mathematics

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What expression is equivalent to (sin^2x) - (sin x) -2 / sin x-2 ?

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HomertheGenius HomertheGenius

01-08-2017

The best way to solve this is to substitute: sin x = t.
So:
( t² - t - 2 ) / ( t - 2 ) =
= ( t² - 2 t + t - 2 ) / ( t - 2 ) =
= ( t ( t - 2 ) + ( t - 2 ) ) / ( t - 2 ) =
= ( t - 2 ) ( t + 1 ) / ( t - 2 ) =
= t + 1 = sin x + 1
Answer: sin x + 1

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