## lsugano 3 years ago what is cot2a=0 Thus 2a=90˚....how did this happen?

1. Mimi_x3

$cot2a = 0 => \frac{cos2a}{sin2a} = 0 => cos2a = 0 => 2a = cos(0)$

2. Mimi_x3

wait i made a typo: $2a = cos^{-1}(0)$

3. Mimi_x3

since you know that $$cos^{-1}(0) = 90$$

4. Mimi_x3

then $$2a = 90$$

5. lsugano

wait how did cot2a= cos2a/sin2a?

6. waterineyes

Firstly you should remember that: $\cos(90) = 0$

7. Mimi_x3

because $cota = \frac{cosa}{sina}$

8. waterineyes

*cot

9. waterineyes

$\large \cot(90^{\circ}) = 0$

10. waterineyes

So you can replace 0 with cot(90): $\cot(2a) = \cot(90)$

11. lsugano

im sorry but isnt cot= 1/tana?

12. Mimi_x3

well you can use that method if you remember whats cot(90)

13. waterineyes

Now as trigonometric ratio is same: So you can equate the angles: $2a = 90$

14. Mimi_x3

yes it because what tana?

15. Mimi_x3

what is*

16. Mimi_x3

yes it is but whats tan(a) then?*

17. lsugano

oh cot also equals to x/y so cos/sin right??

18. waterineyes

Right..

19. lsugano

ohhhh okay it makes sense

20. lsugano

so i get that cos2a/sin2a = 0 but then what is next?

21. Mimi_x3

i typed the solution for you already..

22. waterineyes

Multiply by sin(2a) both the sides..

23. lsugano

so it becomes cos2a (sin2a) = 0 (sin2a)

24. waterineyes

No.. There is one sin(2a) in the denominator too..

25. waterineyes

Can't you cancel sin(2a) with sin(2a) on left hand side ??

26. lsugano

so does it become like this?

27. waterineyes

Yep..

28. lsugano

oh okay now i get the steps! thank you so much @waterineyes @Mimi_x3

29. waterineyes

Welcome dear..