1) If θ is a fixed real number with 0≤θ<2π Show that for all real x, cos(x)+cos(x+θ)=Acos(x+φ) where φ=θ/2 and A=2cos(θ/2) 2) Determine θ if A=1/4 and if A=-1?
I would really appreciate any help... Part should be related with compound angle formulae cos(α+β) and cos(α-β)
I would really appreciate any help... Part should be related with compound angle formulae cos(α+β) and cos(α-β)
3 Answers
If
for
If
for
Explanation:
Using prosthaphaeresis formula:
could obtain:
then:
If
General solution:
for
If
General solution:
for
Note that in both cases the period is
Please see below.
Explanation:
As
=
=
=
where
(a) if
or
hence
and
(b) if
or
hence
and
First part is already proved by Mr.Shwetank Mauria and Mr. Dhilak.
Explanation:
First part is proved .So we determine
Now,
We have,
But ,
So,
Note:
For,