Mathematics: Verify identity list steps. cot(t)(1-cos^2(t))=cos(t)sin(t)

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

Ответ:

varonadestiny1109

01.01.2022

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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Ответ:

Jeiku3629

15.02.2023

Mathematics

y=−2(x−3)2+10

y=−2x2+12x−8

Step-by-step explanation:

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

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