Radical ((1-sinx)/(1+sinx))= (1-sinx)/cosx (absolute)
Simplify
Identity the identity i meant
Note that if you multiply on the left inside the radical, by (1-sinx)/(1-sinx), you have
√((1-sinx)^2/(1-sin^2(x))
That should get you most of the way there, since √x^2 = |x|
To simplify the given expression, let's first look at the numerator of the expression inside the radical, which is (1 - sin(x)).
To simplify it, we can use the identity: (a - b)(a + b) = a^2 - b^2.
In this case, let's consider a = 1 and b = sin(x). Applying the identity, we have:
(1 - sin(x))(1 + sin(x)) = 1^2 - sin^2(x) = 1 - sin^2(x).
Now, let's consider the denominator of the expression inside the radical, which is (1 + sin(x)).
Next, recall the identity: sin^2(x) + cos^2(x) = 1.
Rearranging this identity, we can express cos^2(x) as 1 - sin^2(x).
Substituting this into the denominator of the expression, we have cos^2(x) = 1 - sin^2(x).
Now, substituting both the numerator and the denominator of the expression inside the radical with the simplified expressions we obtained, we have:
√((1 - sin(x))/(cos(x))) = √((1 - sin^2(x))/(cos^2(x))).
Since cos^2(x) = 1 - sin^2(x), we can substitute that into the expression:
√((1 - sin^2(x))/(1 - sin^2(x))).
Simplifying further, we have:
√(1/1) = 1.
So, the simplified form of the given expression is 1.