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9. Explain the given trigonometric equation by matching correct options

Answer variants:

(\frac{1}{\sin X} - \sin X) (\frac{1}{\cos X} - \cos X) (\frac{\sin X}{\cos X} + \frac{\cos X}{\sin X})

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

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

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

(\frac{\cos^{2} X}{\sin X}) (\frac{\sin^{2} X}{\cos X}) (\frac{1}{\sin X \cos X})

(\frac{1}{\sin X} - \sin X) (\frac{1}{\cos X} - \cos X) (\frac{\sin X}{\cos X} + \frac{\sin X}{\cos X})

Prove that

(cosec X - \sin X) (\sec X - \cos X) (\tan X + \cot X)

\(=\)

1

Proof:

LHS \(=\)

(cosec X - \sin X) (\sec X - \cos X) (\tan X + \cot X)

\(=\)

1

\(=\) RHS

Did you find an error?