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Verifying Trig Identities 1730 Views


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Description:

Verifying trig identities is important, especially when you're about to let one of them into the country—which is why they should keep their passports on them at all times.

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Transcript

00:00

verifying trig identities a la shmoop. hemlock Jones has been competing for

00:09

respect as a detective all of which adult life but he is always outshined by [Jones in town square]

00:14

that pesky Sherlock Holmes if only there was a larger problem I could solve then [Jones in victorian apartment]

00:21

I could get the key to the city Jones Jones we've got to solve this riddle the

00:26

save candy looks different tis true but actually the same proved [Wilson walks in]

00:32

their equality or it's over for your Dame cosine X plus sin x times tangent

00:39

X what do you make of it sounds like nonsense to me we must share that the

00:49

sum of cosine X and sine X you verify this trig identity we will substitute [Jones at chalkboard]

00:59

other known trig identities until we have equal sides to all equation we can

01:06

substitute sine x over cosine X for tangent X when we multiply sine X by

01:12

sine x over cosine X we get that cosine of X plus the fraction sine x over

01:20

cosine x sine x equals secant X what is it when we take in value times itself

01:30

squared Oh precisely my boy since we have the product of sines in the second

01:36

term we can simplify to cosine of X plus the fraction sine squared of X divided

01:43

by cosine of X equals secant X now what do I do we know the cosine squared X

01:52

plus sine squared X equals 1 how could I get 2 cosine squared X plus sine squared [math book]

01:58

X equals 1 on the left hand side oh I know we can multiply the left-hand [Jones on victorian couch]

02:03

side by the fraction cosine x over cosine X we get cosine squared of X [chalk board]

02:09

divided by cosine of X plus the fraction cosine X over cosine X times sine

02:15

squared X over cosine x equals secant X since cosine x over cosine X is just a

02:23

fancy way to write one we really just multiplying left side by one wrong if we

02:28

simplify the crazy left hand side we get cosine squared of X plus sine squared of

02:32

x over cosine of x equals secant of X cosine squared plus sine squared equals

02:37

one so we get 1 divided by cosine X equals secant X and the definition of [math book]

02:44

secant of X is 1 divided by the cosine of X so we have small problem

02:49

later that day candy is back in hemlocks on my hero [Jones and Candy on the couch]

02:53

oh it was nothing my dear I'm always looking out for any victim of

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