Question

Below is an attempt to simplify the statement $\cos^4(t) - \sin^4(t)$. The attempt below has a mistake. Identify the initial mistake and explain how to fix only the initial mistake. $\cos^4(t) - \sin^4(t) = (\cos^2(t) - \sin^2(t))(\cos^2(t) + \sin^2(t))$ $= (\cos^2(t) - \sin^2(t))(1)$ $= (\cos^2(t) - (\cos^2(t) - 1))(1)$ $= (\cos^2(t) - \cos^2(t) + 1)(1)$ $= (0 + 1)(1)$ $= 1$

Name: below is an attempt to simplify the statement cos4t sin4t the attempt below has a mistake identify the initial mistake and explain how to fix only the initial mistake cos4t sin4t cos2t sin2t 47371
Uploaded: 2020-06-17T17:29:24-08:00
Duration: 1 min 12 s
Channel: Sarah Lewites
Description: below is an attempt to simplify the statement cos4t sin4t the attempt below has a mistake identify the initial mistake and explain how to fix only the initial mistake cos4t sin4t cos2t sin2t 47371

          Below is an attempt to simplify the statement $\cos^4(t) - \sin^4(t)$. The attempt below has a mistake. Identify the initial mistake and explain how to fix only the initial mistake.
$\cos^4(t) - \sin^4(t) = (\cos^2(t) - \sin^2(t))(\cos^2(t) + \sin^2(t))$
$= (\cos^2(t) - \sin^2(t))(1)$
$= (\cos^2(t) - (\cos^2(t) - 1))(1)$
$= (\cos^2(t) - \cos^2(t) + 1)(1)$
$= (0 + 1)(1)$
$= 1$

below is an attempt to simplify the statement cos4t sin4t the attempt below has a mistake identify the initial mistake and explain how to fix only the initial mistake cos4t sin4t cos2t sin2t 47371

Added by Tony M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sarah Lewites

06/17/2020

Step 1

The given simplification steps are: 1. $\cos^4(t) - \sin^4(t) = (\cos^2(t) - \sin^2(t))(\cos^2(t) + \sin^2(t))$ 2. $= (\cos^2(t) - \sin^2(t))(1)$ 3. $= (\cos^2(t) - (\cos^2(t) - 1))(1)$ 4. $= (\cos^2(t) - \cos^2(t) + 1)(1)$ 5. $= (0 + 1)(1)$ 6. $= 1$ Let's Show more…

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Below is an attempt to simplify the statement $\cos^4(t) - \sin^4(t)$. The attempt below has a mistake. Identify the initial mistake and explain how to fix only the initial mistake. $\cos^4(t) - \sin^4(t) = (\cos^2(t) - \sin^2(t))(\cos^2(t) + \sin^2(t))$ $= (\cos^2(t) - \sin^2(t))(1)$ $= (\cos^2(t) - (\cos^2(t) - 1))(1)$ $= (\cos^2(t) - \cos^2(t) + 1)(1)$ $= (0 + 1)(1)$ $= 1$