Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation

1 + sec^2(x) sin^2(x) = sec^2(x)

Answer 1

please help!! so lost!!

Answer 2

rewrite everything in terms of sine and cosine

Answer 3

huh?

Answer 4

im just st

Answer 5

rewrite sec^2(x) in terms of cosine

Answer 6

starting to learn all this so im still so comfused

Answer 7

u do know the six trig functions right?

Answer 8

kinda.. not memorized

Answer 9

-_-
you kinda HAVE to memorize those for this section

Answer 10

okay so what does sec^2x = ?

Answer 11

1/cos^2x

Answer 12

okay now plug that into sec^2(x)
for these types of questions, simplify the "funny looking" or the longer side first

Answer 13

so plug that into the left side

Answer 14

now im comfused.. i have to make the right side of the equation match the left

Answer 15

yeah. forget about the right side for now. pretend it's not there for now.
just plug in 1/cos^2(x) into sec^2(x) on the left side

Answer 16

like this
\[1+\frac{ 1 }{\cos^2x }(\sin^2x)\]

Answer 17

ohhokay

Answer 18

now just simplify everything
and use one of the pythagorean identies in your last step

Answer 19

im not really sure how to do all that

Answer 20

simplify
\[1+\frac{ 1 }{\cos^2x }(\sin^2x)\]

Answer 21

i feel stupid lol i dont no really how to

Answer 22

it's ok.
\[1+\frac{ \sin^2x }{\cos^2x }\]
just multiply the sin^2(x) in

Answer 23

ohokay

Answer 24

where do i go from there?

Answer 25

sin^2(x)/cos^2(x) = ?

Answer 26

hmm

Answer 27

sin(x)tan(x) ??

Answer 28

wait.. no its..

Answer 29

x sec(2) sin^2(x)

Answer 30

?

Answer 31

just simplify this for now
\[1+\frac{ \sin^2x }{\cos^2x }\]
don't worry about the 1

just simplify
\[\frac{ \sin^2x }{\cos^2x }\]

Answer 32

im not sure really how to

Answer 33

ohh
you do know that sin^2(x)/cos^(2)x = tan^2(x) right?

Answer 34

oh yes

Answer 35

?

Answer 36

yeah this section is all about algebraic manipulation.
then you have this right?
\[1+\tan^2x \]
use one of the pythagorean identities.

Answer 37

1 + tan2u = sec2u

Answer 38

yep.
you have the answer!

Answer 39

wait.. thats the answer?

Answer 40

yeah. you proved that the left side is equal to right side.
lol it's called trig proofs for a reason

Answer 41

so all i put is 1 + tan2u = sec2u for the answer?

Answer 42

just write out the work

Answer 43

ok
thank you

Answer 44

no problem!