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The value of $$\frac{{\sin A}}{{\cot A + {\text{cosec}}\,A}} - \frac{{\sin A}}{{\cot A - {\text{cosec}}\,A}} - 1{\text{ is:}}$$

The value of $$\frac{{\sin A}}{{\cot A + {\text{cosec}}\,A}} - \frac{{\sin A}}{{\cot A - {\text{cosec}}\,A}} - 1{\text{ is:}}$$ Correct Answer 3

$$\eqalign{ & \frac{{\sin A}}{{\cot A + {\text{cosec}}\,A}} - \frac{{\sin A}}{{\cot A - {\text{cosec}}\,A}} - 1 \cr & = \sin A\left - 1 \cr & = \frac{{ - 2\sin A.{\text{cosec}}\,A}}{{ - 1}} + 1 \cr & = 2 + 1 \cr & = 3 \cr} $$

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