Question

Use what you know about trigonometric ratios to show that this equation is
an identity.

Answer 1

Sin (x)=cos (x) * tan (x)

Answer 2

doesnt make sense to me

Answer 3

you know that tanx = sinx/ cosx/

Answer 4

substitute the sin cos tan wid their ratios (opp, adj, hyp)

Answer 5

so sub tanx= sinx/ cosx. this yields left side. left side= right side. QED

Answer 6

tanx= sinx/ cos x because tanx by definition is opp/ adj. sinx= opp/ hyp
cos= adj/hyp.

Answer 7

that confused me waay more ^^

Answer 8

just a note

you can use frac{a}{b} in equations to make fractions
ex.
\[\frac{a}{b}\]

Answer 9

work left side separately
work right side separately

show both are equal

Answer 10

\[\tan x = \frac{\sin x}{\cos x}\]

Answer 11

left side :-

sin x = opp/hyp ---------------(1)

Answer 12

Okay, i will take it really slowly.

Answer 13

sinx= opp/ hyp= left side.

Answer 14

take the right side, substitute opp/adj/hyp, simplify and see if u can get the same as left side

Answer 15

cosx= adj/ hyp; tan x= opp/adj .
cosx* tanx= (adj/hyp) (opp/adj); notice adj can be cancelled out--> opp/ hyp= sinx. Notice it is same as sinx= left side.

Answer 16

\[\frac{ adj }{ hyp }*\frac{ opp }{ adj}\] im really confused :/

Answer 17

keep going, one more step. confusion wil go away

Answer 18

adj/adj = 1

Answer 19

top adj can be cancelled out with bottom adj, and you are left with opp/hyp= sinx

Answer 20

ok so i was almost there \[\sin (x)=\frac{ opp }{ hyp }\]

Answer 21

like that

Answer 22

brb yall meh baby is hungry

Answer 23

the other way is to say
\[ \tan(x) = \frac{\sin(x)}{\cos(x)}\]

replace tan(x) in
\[ \sin(x)= \cos(x) \tan(x) \\ \sin(x)= \cos(x)\frac{\sin(x)}{\cos(x)}\]
then notice that cos(x)/cos(x) is 1 you get
\[ \sin(x)=\sin(x) \]

Answer 24

Right hand side :-

\(\large \frac{ adj }{ hyp }*\frac{ opp }{ adj} \)

\(\large \frac{ \cancel{adj} }{ hyp }*\frac{ opp }{ \cancel{adj}} \)

\(\large \frac{ opp }{ hyp } \) ------------(2)

Answer 25

from (1) and (2), left hand side = right hand side. so its an identity.

Answer 26

oh ok so how do i write it into words

Answer 27

you wanto write math into words ? hmm

Answer 28

just showing the proof wont do ha ?

Answer 29

no i have to write it into words :(

Answer 30

okay then describe wat we just did, you may start like below :-

since left hand side is sinx, and we knw that sinx = opp/hyp, proving right hand side simplifies to opp/hyp is sufficient to prove that given equation is an identity. right hand side we have cosx * tanx. substituting their respective trig ratios, we get adj/hyp * opp/adj....

Answer 31

ty

Answer 32

np, im sure you can conclude :)

Answer 33

yea i think i can :D

Answer 34

@phi @katherine.ok @ganeshie8 thank you all for for help