How would you solve this problem?
cos x/1+sinx
To solve this problem, we need to simplify the expression cos(x) / (1 + sin(x)).
Step 1: Start by multiplying both the numerator and denominator of the expression by (1 - sin(x)). This will help us simplify the expression.
cos(x) / (1 + sin(x)) * (1 - sin(x)) / (1 - sin(x))
Step 2: Simplify the expression using the distributive property.
cos(x) * (1 - sin(x)) / ((1 + sin(x)) * (1 - sin(x)))
Step 3: Simplify further by expanding the denominator.
cos(x) * (1 - sin(x)) / (1 - sin^2(x))
Step 4: Recall the Pythagorean identity sin^2(x) + cos^2(x) = 1.
cos(x) * (1 - sin(x)) / (1 - sin^2(x))
cos(x) * (1 - sin(x)) / cos^2(x)
Step 5: Simplify by canceling out the common factor of cos(x).
(1 - sin(x)) / cos(x)
So, the simplified expression is (1 - sin(x)) / cos(x).