## highschoolmom2010 2 years ago Use what you know about trigonometric ratios to show that this equation is an identity.

1. highschoolmom2010

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

2. highschoolmom2010

doesnt make sense to me

3. katherine.ok

you know that tanx = sinx/ cosx/

4. ganeshie8

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

5. katherine.ok

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

6. katherine.ok

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

7. highschoolmom2010

that confused me waay more ^^

8. completeidiot

just a note you can use frac{a}{b} in equations to make fractions ex. $\frac{a}{b}$

9. ganeshie8

work left side separately work right side separately show both are equal

10. completeidiot

$\tan x = \frac{\sin x}{\cos x}$

11. ganeshie8

left side :- sin x = opp/hyp ---------------(1)

12. katherine.ok

Okay, i will take it really slowly.

13. katherine.ok

sinx= opp/ hyp= left side.

14. ganeshie8

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

15. katherine.ok

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.

16. highschoolmom2010

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

17. ganeshie8

keep going, one more step. confusion wil go away

18. phi

19. katherine.ok

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

20. highschoolmom2010

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

21. highschoolmom2010

like that

22. highschoolmom2010

brb yall meh baby is hungry

23. phi

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 $\sin(x)=\sin(x)$

24. ganeshie8

Right hand side :- $$\large \frac{ adj }{ hyp }*\frac{ opp }{ adj}$$ $$\large \frac{ \cancel{adj} }{ hyp }*\frac{ opp }{ \cancel{adj}}$$ $$\large \frac{ opp }{ hyp }$$ ------------(2)

25. ganeshie8

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

26. highschoolmom2010

oh ok so how do i write it into words

27. ganeshie8

you wanto write math into words ? hmm

28. ganeshie8

just showing the proof wont do ha ?

29. highschoolmom2010

no i have to write it into words :(

30. ganeshie8

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....

31. highschoolmom2010

ty

32. ganeshie8

np, im sure you can conclude :)

33. highschoolmom2010

yea i think i can :D

34. highschoolmom2010

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