Solving Identities
[(1+tanx)/(sinx)]- secx
I got cscx please halp me to solve it to see if its right
To solve the given expression, we need to simplify it step by step. Here's how you can do it:
Step 1: Let's simplify the expression [(1 + tan(x)) / sin(x)] - sec(x).
Step 2: Using the reciprocal identity, we can rewrite sec(x) as 1/cos(x).
So the expression becomes [(1 + tan(x)) / sin(x)] - (1 / cos(x)).
Step 3: To combine the fractions, we need a common denominator.
Multiply the first fraction by cos(x) / cos(x) and the second fraction by sin(x) / sin(x) to get:
[(1 + tan(x)) * cos(x) / (sin(x) * cos(x))] - [(1 * sin(x)) / (cos(x) * sin(x))].
This simplifies to [(cos(x) + sin(x) * cos(x)) / (sin(x) * cos(x))] - [sin(x) / sin(x)].
Step 4: Simplify the expression by canceling out common factors:
[(cos(x) + sin(x) * cos(x)) / (sin(x) * cos(x))] - [sin(x) / sin(x)]
cos(x) / (sin(x) * cos(x)) = 1 / sin(x) = csc(x).
So the expression simplifies to:
cos(x) + sin(x) * cos(x) - 1 = cos(x) + cos(x) * sin(x) - 1.
So the simplified expression is cos(x) + cos(x) * sin(x) - 1.
Therefore, csc(x) is not the final answer.