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Ivenika [448]
3 years ago
7

How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ

Mathematics
1 answer:
sattari [20]3 years ago
8 0
<h3>Explanation:</h3>

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

  cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

  (1 -sin^2(θ))cot^2(θ) =  . . . . . replace cos^2 with 1-sin^2

  cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

  cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

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Step-by-step explanation:

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