prove that trigonometry is a branch representative or teller line segment
Answers
Answer:
he friend can I know in which class you study and from which school
Tip 1) Always Start from the More Complex Side.
Tip 2) Express everything into Sine and Cosine.
Tip 3) Combine Terms into a Single Fraction.
Tip 4) Use Pythagorean Identities to transform between sin²x and cos²x.
Tip 5) Know when to Apply Double Angle Formula (DAF)
Tip 6) Know when to Apply Addition Formula (AF)
Answer:
From the first principles, we define the complex exponential function as a complex function
f
(
z) that satisfies the following defining
properties:
1.
f
(
z) is entire,
2.
f
′(
z) =
f
(
z),
3.
f
(
x) =
e
x, x is real.
Let
f
(
z) =
u
(x, y) + iv
(x, y),
z
=
x
+ iy. From property (1),
u and
v satisfy the Cauchy-Riemann relations. Combining (1) and (2
)
u
x
+ iv
x
=
v
y
− iu
y
=
u
+ iv.
First, we observe that
u
x
=
u and
v
x
=
v and so
u
=
e
x
g
(
y) and
v
=
e
x
h
(
y
),
where
g
(
y) and
h
(
y) are arbitrary functions in
y.
1
We also have
vy = u and uy = −v,
from which we deduce that the arbitrary functions are related by
h′(y) = g(y) and − g′(y) = h(y).
By eliminating g(y) in the above relations, we obtain
h′′(y) = −h(y).
The general solution of the above equation is given by
h(y) = A cos y + B sin y,
where A and B are arbitrary constants. Furthe
Step-by-step explanation: