cosθ/sinθ
To simplify the expression cosθ/sinθ, we can first recall some trigonometric identities
To simplify the expression cosθ/sinθ, we can first recall some trigonometric identities.
We know that the cosine of an angle θ is equal to the adjacent side divided by the hypotenuse in a right triangle. Therefore, cosθ = adjacent/hypotenuse.
Similarly, the sine of an angle θ is equal to the opposite side divided by the hypotenuse in a right triangle. Therefore, sinθ = opposite/hypotenuse.
Now, let’s substitute these values into the expression cosθ/sinθ:
cosθ/sinθ = (adjacent/hypotenuse) / (opposite/hypotenuse)
Since we have a common denominator (hypotenuse) in both the numerator and denominator, we can simplify the expression further:
cosθ/sinθ = (adjacent/hypotenuse) * (hypotenuse/opposite)
The hypotenuse cancels out, and we are left with:
cosθ/sinθ = adjacent/opposite
Therefore, the simplified form of cosθ/sinθ is simply the ratio of the adjacent side length to the opposite side length in a right triangle.
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