Final answer:
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:
- Write tanθ as sinθ/cosθ.
- tanθ/sinθ = (sinθ/cosθ) / sinθ
- Cancel out sinθ from the numerator and the denominator.
- What remains is 1/cosθ, which is the definition of secθ.
Therefore, tanθ/sinθ simplifies to secθ.