Open Question: How do you prove the following identity? : (1/sin x) - ((cos^2 x)/ (sin x) = sin x?
8:05 Publicado por Anónimo
Start by combining the fractions to get:
LHS = 1/sin(x) - cos^2(x)/sin(x)
= [1 - cos^2(x)]/sin(x).
LHS = 1/sin(x) - cos^2(x)/sin(x)
= [1 - cos^2(x)]/sin(x).
Then, since sin^2(x) + cos^2(x) = 1 ==> sin^2(x) = 1 - cos^2(x):
LHS = [1 - cos^2(x)]/sin(x)
= sin^2(x)/sin(x)
= sin(x), by canceling sin(x)
= RHS.
I hope this helps!
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