Stuck :( (1 Viewer)

[Faera]

Okay guys, it's a pretty stupid question, because of the not being allowed to use the double angle rule, but I just cannot see any other way of doing it!

If you can come up with a solution, it would be absolutely wonderful!

Thanks in advance.


Prove that:
tan[2@] + cot@ = sec[2@] * cot@

Without using double angel results.


thanks!

 

[Calculon]

sin2@/cos2@ + cos@/sin@ = cos@/(cos2@sin@)
(sin2@sin@ + cos@cos2@)/sin@cos2@=cos@/cos2@sin@
sin2@sin@ + cos2@cos@ = cos@
sin2@tan@ + cos2@= 1
sin2@tan@ + cos2@ = sin²2@ + cos²2@
tan@ = sin2@ + cos2@

and now I'm lost. Try the t method maybe?

 

[CM_Tutor]

You could use calculus - show that d/d@(LHS) = d/d@(RHS), and so LHS = RHS + C, for some constant C. Then, by putting @ = pi / 6, show that C = 0.

Note - I haven't written this out, so I'm not sure that you can easily show d/d@(LHS) = d/d@(RHS) without double angle formulae.

Originally posted by [FTHRW8]
t method?

This is another possibiliy, but it is arguable as the t-method is really based on double angle formulae.

 

[Faera]

Thanks for the help, guys.

CM's method works! (very smart!)

yayyyyyy!

=D

thanks!

 

[Affinity]

What about straight trig.

cos(2x - x) = cos(x)

cos(2x)cos(x) + sin(2x)sin(x) = cos(x)

divide both sides by cos(2x)sin(x)

cos(x)/sin(x) + sin(2x)/cos(2x) = cos(x)/sin(x) * 1/cos(2x)

cot(x) + tan(2x) = cot(x) * sec(2x)

 

[CM_Tutor]

Affinity,

Originally posted by Faera
Without using double angel results.

otherwise, I'd agree with you

 

[Affinity]

look again, I changed it

 

[CM_Tutor]

Originally posted by Affinity
cos(2x - x) = cos(x)

cos(2x)cos(x) + sin(2x)sin(x) = cos(x)

How is using the result cos(2x - x) = cos(2x)cos(x) + sin(2x)sin(x) not using a double angle formula?

 

[Affinity]

the double angle formulae are

cos(2x) = [cos(x)]^2 - [sin(x)]^2
sin(2x) = 2sin(x)cos(x)
tan(2x) = 2tan(x)/(1-tan(x)^2)

the result there is a difference of angles formula

 

[CM_Tutor]

OK, but I think that is hair splitting. Anyway ...

 

[Affinity]

 

[Grey Council]

lol

 

[Xayma]

Hmm great now theres argument about meaning of words in Maths, BOS is going to far.