Simplify: csc A - sin A - Cot A
Cot A Csc A
1/sin - sin A - 1/tan
1/tan 1/sin
-sinA?
rewrite all in terms of sines and cosines, find a common denominator and "simplify".
BTW, I got it as far as
cotA(cosA - 1)
To simplify the expression csc A - sin A - Cot A / Cot A - Csc A, we need to first simplify the numerator (csc A - sin A - Cot A) and the denominator (Cot A - Csc A) separately.
Let's start with the numerator:
csc A - sin A - Cot A
To simplify this, we need to rewrite the terms using trigonometric identities.
1. Cot A can be written as 1/tan A:
csc A - sin A - 1/tan A
2. Cosecant (csc A) can be written as 1/sin A:
1/sin A - sin A - 1/tan A
Now, let's simplify the denominator: Cot A - Csc A
First, we'll rewrite Cot A as 1/tan A:
1/tan A - Csc A
The next step is to find a common denominator for the terms in both the numerator and denominator. The common denominator will be sin A * tan A.
Now, let's simplify the expression using the common denominator.
Numerator:
(1/sin A) - (sin A * tan A)/sin A - (1/tan A)
The sin A in the second term cancels out, so we have:
1/sin A - tan A - 1/tan A
The denominator remains:
(1/tan A) - (1/sin A)
Now, combine like terms in the numerator:
(1/sin A) - tan A - (1/tan A)
Multiplying both terms by sin A, we get:
1 - (sin A * tan A) - sin A
Next, simplify the denominator:
(1/tan A) - (1/sin A)
Multiplying both terms by tan A, we get:
1 - (sin A * tan A) - sin A
Now, we can simplify the expression by combining like terms in the numerator and denominator.
The final simplified expression is:
(1 - 2sin A * tan A) / (tan A - sin A)