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Goryan [66]
3 years ago
11

Verify identity list steps. Cot(t)(1-cos^2(t))=cos(t)sin(t)

Mathematics
1 answer:
storchak [24]3 years ago
4 0
Remember: We have to work from either the LHS or the RHS.
(Left hand side or the Right hand side)

You should already know this:

\huge{Cot(t) = \frac{1}{tan(t)} = \frac{1}{\frac{sin(t)}{cos(t)}} = 1\div \frac{sin(t)}{cos(t)} = 1\times \frac{cos(t)}{sin(t)}=\boxed{\frac{cos(t)}{sin(t)}}


You should also know this:

sin^2(t) + cos^2(t) = 1\\\\\boxed{sin^2(t)} = 1 - cos^2(t)

So plugging in both of those into our identity, we get:

\frac{cos(t)}{sin(t)}\cdot sin^2(t) = cos(t)\cdot sin(t)

Simplify the denominator on the LHS (Left Hand Side)

We get:

cos(t) \cdot sin(t) = cos(t) \cdot sin(t)

LHS = RHS

Therefore, identity is verified.
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