(Cos/1-sin)- tan
You clearly did not even look at my previous post in reply to a similar question.
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To simplify the expression (cos/1-sin) - tan, we can follow these steps:
Step 1: Simplify the term cos/(1 - sin).
The expression cos is the abbreviation for cosine, which is a trigonometric function. To simplify this term, we need to consider the trigonometric identity:
sin^2(x) + cos^2(x) = 1
Rearranging this equation, we can isolate cos(x):
cos^2(x) = 1 - sin^2(x)
Taking the square root of both sides, we get:
cos(x) = √(1 - sin^2(x))
Now, we can substitute this value into the original expression:
cos/(1 - sin) = (√(1 - sin^2))/(1 - sin)
Step 2: Simplify the term (√(1 - sin^2))/(1 - sin).
We can simplify this expression by rationalizing the denominator. To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is (1 + sin):
(√(1 - sin^2))/(1 - sin) * (1 + sin)/(1 + sin)
Expanding the numerator, we get:
√(1 - sin^2) * (1 + sin)
Simplifying further, we have:
√(1 - sin^2) + √(sin^2 - sin^3)
Step 3: Simplify the term tan.
The term tan is the abbreviation for tangent, which is also a trigonometric function. To simplify the expression, we need to recall the identity:
tan(x) = sin(x)/cos(x)
Now, we can substitute this value into the original expression:
tan = sin/cos
Step 4: Combine the simplified terms.
The expression now becomes:
(√(1 - sin^2) + √(sin^2 - sin^3)) - (sin/cos)