Question

trig proofs

Answer 1

@supie
@AZ
@boredfr

Answer 2

Ok so what do you have so far or do you need everything?

Answer 3

I get 0 of it

Answer 4

Um ok so let's start with the first one

secx-tanxsinx=1/secx

First we manipulate the left side
sec(x)-tan(x)sin(x)

Do you understand so far?

Answer 5

Yes, it's just the left

Answer 6

Ok so now we are gonna apply the trig identity
1/sec(0 )= cos(0)

sec(x)-tan(x)sin(x)-cos(x)

Understand still?

Answer 7

i think that i'm just supposed to do the left, ignore the right, just manipulate the left side to bring it to the right side of the equation?

Answer 8

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
i think that i'm just supposed to do the left, ignore the right, just manipulate the left side to bring it to the right side of the equation?
\(\color{#0cbb34}{\text{End of Quote}}\)
That was the purpose of the first step yes

Answer 9

But you brought the right side over to the left

Answer 10

Ok wait no you manipulate the left side but beyond that I cant explain in words just numbers so @AZ

Answer 11

Hi

so first let's use some basic identities

sec x = 1/cos x

tan x = sin x/ cos x

what do you get if you add the fractions

\(\dfrac{1}{\cos x} - \left(\dfrac{\sin x}{\cos x}\times \sin x\right)= \dfrac{1}{\sec x}\)

Answer 12

yea, i get that

Answer 13

what is

1 - sin^2x

hint:
\(\ sin^2 (x) + \cos^2 (x) = 1\)

Answer 14

cosx^2

Answer 15

yeah and your denominator is cos (x)

so what is

cos^2 (x) / cos(x)

Answer 16

cosx?

Answer 17

x?

Answer 18

yup

and what is 1/sec (x)

remember sec(x) = 1/cos(x)

so what is 1/sec(x) =

Answer 19

basically to prove the identity, you show that the LHS (left hand side) equals the RHS (right hand side)

Answer 20

*confused*
\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
what is

1 - sin^2x

hint:
\(\ sin^2 (x) + \cos^2 (x) = 1\)
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
yeah and your denominator is cos (x)

so what is

cos^2 (x) / cos(x)
\(\color{#0cbb34}{\text{End of Quote}}\)


where?

Answer 21

You understood this part, right?

\(\dfrac{1}{\cos x} - \left(\dfrac{\sin x}{\cos x}\times \sin x\right)= \dfrac{1}{\sec x}\)

so when you multiply, you get this

\(\dfrac{1}{\cos x} - \dfrac{\sin^2 x}{\cos x}= \dfrac{1}{\sec x}\)


and that's how we proceeded

Answer 22

ohhhhhhhhhh, okay lol

Answer 23

so do you get how to finish the question?

you show that the left side was simplified to cos(x) and that the right side can also be simplified to cos(x)

Answer 24

yep, i do

Answer 25

perfecto

Answer 26

heh

do you want me to post another question for the next?

Answer 27

sure