Question

Simplify to a single trig function with no denominator.
tanθ/sinθ

Answer 1

To simplify tanθ/sinθ, recognize that tanθ equals sinθ/cosθ. Dividing by sinθ cancels it out, leaving 1/cosθ, which is known as secθ.

Step-by-step explanation:

To simplify the expression tanθ/sinθ to a single trig function with no denominator, we use the fundamental trigonometric identities. Recall that tanθ is equal to sinθ/cosθ. Therefore, when we divide tanθ by sinθ, sinθ cancels out, leaving us with 1/cosθ, which is also known as secθ.

Here is the step-by-step simplification:

1. Write tanθ as sinθ/cosθ.
2. tanθ/sinθ = (sinθ/cosθ) / sinθ
3. Cancel out sinθ from the numerator and the denominator.
4. What remains is 1/cosθ, which is the definition of secθ.

Therefore, tanθ/sinθ simplifies to secθ.