7. Explain the given trigonometric equation by matching correct options

Answer variants:

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

(\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})

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?