## saifoo.khan 3 years ago Easy trig problem below:

1. jasonxx

?

2. saifoo.khan

$\frac{3A}{sinA} + \frac{\cos3A}{\cos A}≡ 4 \cos 2A$

3. jasonxx

cos(3A) = cos(2A+A) =4 cos³ A - 3 cos A

4. jasonxx

taking the LCM and then using 2 sinA * cos A= sin 2A

5. jasonxx

and cos 2A= cos^2 2A -1

6. saifoo.khan

I'm not sure about your working but i completed till here: $\frac{\cos A \sin 3A + \cos 3A \sin A}{\sin A \cos A}$

7. saifoo.khan

Then: $\frac{\sin(A+3A)}{\sin A \cos A}$idk what to do after this..

8. saifoo.khan

@jasonxx ?

9. jasonxx

well, i guess expand everything

10. zepdrix

$\frac{\sin(4A)}{\frac{1}{2}\sin(2A)}$ This the next step? :) hmm fun problem.

11. zepdrix

$\frac{4\sin(2A) \cos(2A)}{\sin(2A)}$ $=4\cos(2A)$ Something like that... :D Yayyy team!

12. saifoo.khan

HOW? HOW? HOW?

13. jasonxx

sin(4A)=sin(2* 2A)

14. zepdrix

Oh like say what each step that's being performed? :D

15. saifoo.khan

Last 3 steps, yes sir. @zepdrix ;D

16. jasonxx

and sin (2*2A) is like sin (2* X)= 2*2 sin (2A)cos(2A)

17. zepdrix

Hmm so we're taking advantage of Sine's Double Angle Formula, On top, in one direction, on the bottom in the other direction. Yah looks like Jason has the right idea also ^^

18. jasonxx

:)) thanks @zepdrix

19. saifoo.khan

I have this general formula with me: sin2A = 2sinAcosA But how did you guys converted sin4A into this?

20. jasonxx

Let's say A=X then its gona be sin (2X), now X=2A therefore its gona be the conversion mentioned above

21. saifoo.khan

I think i got it now. Thanks @jasonxx and @zepdrix . :)

22. jasonxx

:) keep rockin

23. zepdrix

Oh sorry. I wasn't going into much detail because I thought you were testing us :) lol

24. saifoo.khan

Lol. No. this was the last problem of 26. i had the answers but wasn't getting the last step!

25. saifoo.khan

@zepdrix Where did the 1/2 in your second last step go? D:

26. zepdrix

So we're dividing by a fraction, let's fix that a sec. $\frac{\sin(4A)}{\frac{1}{2}\sin(2A)} \quad = \quad \frac{2\sin(4A)}{\sin(2A)}$ Then we apply the Sine Double Angle Formula to the top part.$\frac{2\sin(2\cdot 2A)}{\sin(2A)} \quad = \quad \frac{2\cdot 2 \sin(2A)\cos(2A)}{\sin(2A)}$

27. saifoo.khan

Oh! Now it makes perfect sense to me!