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Simplify the following expression by using identities. \(\frac{{{{\sin }^2}{\rm{x}} - 1}}{{\sin {\rm{x\;}} + {\rm{\;}}1{\rm{\;}}}}\)

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Simplify the following expression by using identities.

\(\frac{{{{\sin }^2}{\rm{x}} - 1}}{{\sin {\rm{x\;}} + {\rm{\;}}1{\rm{\;}}}}\)


1). sin x
2). cosx
3). -1 + sin x
4). 1 - cosx


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Answered by on | Votes 2 |

$(\because 1 - {\sin ^2}x = \left( {1 - \sin x} \right)\left( {1 + \sin x} \right))$

$(\frac{{\left( { - 1} \right)\left( {1{\rm{\;}} + {\rm{\;sinx}}} \right)\left( {1 - \sin {\rm{x}}} \right)}}{{\sin {\rm{x\;}} + {\rm{\;}}1}} = \sin {\rm{x}} - 1)$

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