Question

Implify the expression. Write the final form with no fractions.

(tan²x+2tanx+1)/(tan²x+tanx) =
​
1- 1+cscx
2 - 1+cotx
3 - 1+tanx
4 - -tanx

Answer 1

To simplify the expression, factor and cancel out common terms in the numerator and denominator. The final simplified form is 1 + cotx.

Step-by-step explanation:

To simplify the expression, we need to factor and cancel out common terms in the numerator and denominator.

We can rewrite the expression as:

(tan²x+2tanx+1)/(tan²x+tanx) = (tanx+1)²/(tanx(tanx+1))

Next, we can cancel out the common factor (tanx+1) in the numerator and denominator:

(tanx+1)²/(tanx(tanx+1)) = (tanx+1)/tanx

Finally, we simplify by dividing the numerator by tanx:

(tanx+1)/tanx = 1 + 1/tanx = 1 + cotx

Therefore, the simplified expression is 1 + cotx.