Trig identity help (1 Viewer)

[Footyking]

hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11

 

[Footyking]

hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 1

 

[braintic]

hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 1

This is an Extension question, not 2 unit.

Do you do Extension, and have you learned the t-results or Auxiliary Angle method?

If not, you can still do it:
Let u=sin2x, so cos2x=sqrt(1-u^2)

The equation becomes 9 Sqrt(1-u^2) = 1-7u

Then square both sides, solve for u, then for x.

And finally as your solution involves squaring, check your answers by substitution, as squaring tends to introduce extra solutions.

 

[braintic]

hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11

Oops, check my response to your question in the 2 unit forum.

 

[Footyking]

Yes i do extension and i have learnt the t results, not the auxiliary angle method. Ive tried using t results and it didnt work for me, thats why i need help.

 

[Footyking]

sorry, i didnt understand the way you did it on the other post. can you do it by the t results? Do you expand the double angle before you use the t results or not?

 

[HeroicPandas]

nvm i am crazy

 

[Footyking]

As stated from braintic's post: "Let u=sin2x, so cos2x=sqrt(1-u^2)"

u = sin 2x

Square both sides,

u^2 = sin^2 (2x)
u^2 = 1 - cos^2 (2x)
cos^2 (2x) = 1 - u^2
cos(2x) = sqrt{1-u^2)

Ok im really sorry but i did not learn how to do it that way, is there a chance you can show me by doing the t results?

 

[braintic]

hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11

Let t=tanx (tan of half the angle)

9(1-t^2)/(1+t^2) + 14t(1+t^2) = 11
9(1-t^2) + 14t = 11(1+t^2)
9 - 9t^2 + 14t = 11 + 11t^2
20t^2 - 14t + 2 = 0
You can solve that for t, replace t by tan x, then solve

 

[HeroicPandas]

nvm i am crazy...