Final answer:
To simplify the expression (tanx/1−tanx) + (cosx/sinx−cosx), find a common denominator and combine the fractions before simplifying.
Step-by-step explanation:
To simplify the expression, (tanx/1−tanx) + (cosx/sinx−cosx), we need to find a common denominator for the fractions. The common denominator for the two fractions is sinx−cosx.
So, multiplying the first term, (tanx/1−tanx), by sinx−cosx/sinx−cosx gives us (tanx(sin x−cosx))/(sin x−cosx).
Similarly, multiplying the second term, (cosx/sinx−cosx), by sinx−cosx/sinx−cosx gives us (cosx(sin x−cosx))/(sin x−cosx).
Now, we can combine the two fractions and simplify further, giving us (tanx(sin x−cosx)+cosx(sin x−cosx))/(sin x−cosx).