Verify that each equation is an identity..
tan A= sec a/csca
I have notes (i wasn't here that day and teacher refuses to reteach) but I don't understand them here is the notes...
Problem w/ same directions:
Cos x= cotx/csc x
= Cosx/Sin x / 1/sinx = cosx
I just don't get this?!?!
What don't you understand?
To prove Cos x = cotx/csc x,
Just rewrite it as
(Cosx/Sin x) / (1/sinx) = cosx
It is just algebra.
Similarly,
tan a = sin a/cos a
= (1/csc a)/(1/sec a) = sec a/csc a
To verify that each equation is an identity, we need to simplify both sides of the equation and show that they are equal.
Let's start with the first equation: tan A = sec A/csc A.
To simplify the right side, we use the definitions of secant and cosecant functions:
sec A = 1/cos A
csc A = 1/sin A
Substituting these values into the equation, we get:
tan A = (1/cos A)/(1/sin A)
Now, we can simplify the right side by multiplying the numerator and denominator by sin A:
tan A = (1/cos A) * (sin A/1)
Multiplying these fractions, we get:
tan A = sin A/cos A
This is a well-known identity, so the equation tan A = sec A/csc A is indeed an identity.
Now, let's move on to the second equation: cos x = cot x/csc x.
First, let's rewrite the right side of the equation:
cot x = 1/tan x (using the definition of cotangent)
csc x = 1/sin x (using the definition of cosecant)
Substituting these values into the equation, we get:
cos x = (1/tan x)/(1/sin x)
Simplifying further, we can multiply the numerator and denominator by sin x and simplify:
cos x = (1/tan x) * (sin x/1)
Multiplying these fractions, we get:
cos x = sin x/tan x
Again, this is a well-known identity, so the equation cos x = cot x/csc x is also an identity.
By following the steps above and simplifying the equations, we have verified that both equations are identities.