Use trigonometric identities to transform the left side of the equation into the right side (0 < θ < π/2). Fill in the blank tan θ cot θ = 1 tan θ cot θ = sin θ/cos θ * blank/sin θ = 1

The identity which should be filled into the blank is cos θ.

From trigonometric identities; we know;

Ultimately, sin θ/cos θ × cos θ/sin θ = 1.

Therefore, the missing identity is cos θ.

Read more on trigonometric identities;

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Cosθ

Step-by-step explanation:

Given the trigonometry identity:

tan θ cot θ = 1, to transform this identity, we need to write in terms of sinθ and cosθ as shown;

In trig:

tanθ = sinθ/cosθ

cotθ = 1/tanθ

1/tanθ = 1/(sinθ/cosθ)

1/tanθ = cosθ/sinθ

Hence cotθ = cosθ/sinθ

Substitute the expression for tanθ and cotθ into the expression in question

tan θ cot θ = 1

sinθ/cosθ*cosθ/sinθ = 1

Comparing the gotten expression with

sin θ/cos θ * blank/sin θ = 1 we can dee that the blank is cosθ

Hence the correct answer is cosθ

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