Answer : (1 - 2sin a) / sin a
Step - by step explanation :
To simplify the expression cos^2a/sin a - 1, we can follow these steps:
1. Rewrite cos^2a as (cos a)^2.
2. Apply the formula (cos a)^2 = 1 - (sin a)^2.
3. Substitute the formula into the expression: [(1 - (sin a)^2) / sin a] - 1.
4. Simplify further by distributing the negative sign: (1/sin a) - (sin a)^2/sin a - 1.
5. Combine the terms with the common denominator: (1 - (sin a)^2 - sin a) / sin a.
6. Simplify the numerator: (1 - sin a - sin a) / sin a.
7. Further simplify: (1 - 2sin a) / sin a.
Therefore, the simplified expression is (1 - 2sin a) / sin a.
