Prove that sinx * csc(-x) = -1
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calendarEducator since 2008
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sinx * csc(-x) = -1
We will use the trigonometric identities to prove the identity.
First, we know that csc(x) = 1/sinx.
==> csc(-x) = 1/sin(-x)
Now we will substitute in the identity.
==> sinx * 1/sin(-x) = -1
Now, we know that sin(-x) = -sinx
==> sinx * 1/-sin(x) = -1
Now we will reduce similar terms.
==> -1 = -1 .............q.e.d
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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have cosec x = 1/sin x.
sin (-x) = -sin x.
Now sin x * cosec(-x)
=> sin x * (1 / sin (-x))
=> sin x * ( -1 / sin x)
=> -1 * (sin x / sin x)
= -1
Therefore we prove that sin x * cosec(-x) = -1
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