# Verifying Trig Identities

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.

 Functions Prove and apply trigonometric identities Geometry Right Triangles and Trigonometry Language English Language Right Triangles and Trigonometry Basic Trig Ratios Trigonometric Functions Basic Trig FunctionsInversesTrigonometric Identities

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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