Question

Simplify tanx−cscx⋅secx⋅tanx⋅cotx to a single trigonometric function.

Answer 1

To simplify the expression tanx−cscx⋅secx⋅tanx⋅cotx to a single trigonometric function, rewrite the expression in terms of sine and cosine only. The simplified expression is (sin(x) - 1)/(cos(x) * sin(x)).

Step-by-step explanation:

To simplify the expression tan(x) - csc(x) * sec(x) * tan(x) * cot(x) to a single trigonometric function, we need to rewrite the expression in terms of sine and cosine only. Here's how:

1. Recall that tan(x) = sin(x)/cos(x), so we can substitute this into the expression to get:
2. sin(x)/cos(x) - csc(x) * sec(x) * sin(x)/cos(x) * cos(x)/sin(x)
3. Simplify the expression:
4. sin(x)/cos(x) - (1/sin(x)) * (1/cos(x)) * sin(x)/cos(x) * cos(x)/sin(x)
5. sin(x)/cos(x) - (1/sin(x)) * (1/cos(x))
6. Combine the fractions:
7. (sin(x) - 1)/(cos(x) * sin(x))

So, the simplified expression is (sin(x) - 1)/(cos(x) * sin(x)).