Show the given trigonometric equation — task. Mathematics State Board, Class 10.

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Answer variants:

\frac{2 \sin x}{\sin^{2} x}

\frac{\sin x + \sin x \cos x + \sin x + \sin x \cos x}{1 - \cos^{2} x}

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

\frac{2 \sin x}{1 - \cos^{2} x}

\frac{2}{\sin x}

\frac{\sin x - \sin x \cos x + \sin x + \sin x \cos x}{1 - \cos^{2} x}

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

Show that

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

\(=\)

2 cosec x

Proof:

LHS \(=\)

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

\(=\)

2 cosec x

\(=\) RHS

Did you find an error?

12. Show the given trigonometric equation