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8. Explain the given trigonometric equation by matching correct options

Answer variants:

$(\frac{\cos^{2} θ}{\sin θ}) (\frac{\sin^{2} θ}{\cos θ}) (\frac{1}{\sin θ \cos θ})$

$(\frac{1}{\sin θ} - \sin θ) (\frac{1}{\cos θ} - \cos θ) (\frac{\sin θ}{\cos θ} + \frac{\sin θ}{\cos θ})$

$(\frac{1}{\sin θ} - \sin θ) (\frac{1}{\cos θ} - \cos θ) (\frac{\sin θ}{\cos θ} + \frac{\cos θ}{\sin θ})$

$(\frac{\cos^{2} θ \times \sin^{2} θ \times 1}{\sin^{2} θ \times \cos^{2} θ})$

$(\frac{1 + \sin^{2} θ}{\sin θ}) (\frac{1 + \cos^{2} θ}{\cos θ}) (\frac{\sin^{2} θ + \cos^{2} θ}{\sin θ \cos θ})$

$(\frac{1 - \sin^{2} θ}{\sin θ}) (\frac{1 - \cos^{2} θ}{\cos θ}) (\frac{\sin^{2} θ + \cos^{2} θ}{\sin θ \cos θ})$

Prove that

$(cosec θ - \sin θ) (\sec θ - \cos θ) (\tan θ + \cot θ)$

$=$

$1$ .

Proof:

LHS

$=$

$(cosec θ - \sin θ) (\sec θ - \cos θ) (\tan θ + \cot θ)$

$=$

$1$

$=$ RHS

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