# Verify the identity \sec\theta\cot\theta-\sin\theta=\frac{\cos^2\theta}{\sin\theta}

Verify the identity $$\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{{\cos}^{{2}}\theta}}}{{{\sin{\theta}}}}}$$

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We Trigonometry identities to verification
$$\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{{\cos}^{{2}}\theta}}}{{{\sin{\theta}}}}}$$
$$\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{1}}}{{{\cos{\theta}}}}}\times{\frac{{{\cos{\theta}}}}{{{\sin{\theta}}}}}-{\sin{\theta}}$$
$$\displaystyle\because{\sec{\theta}}={\frac{{{1}}}{{{\cos{\theta}}}}}$$
$$\displaystyle\because{\cot{\theta}}={\frac{{{\cos{\theta}}}}{{{\sin{\theta}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\sin{\theta}}}}}-{\frac{{{\sin{\theta}}}}{{{1}}}}$$
$$\displaystyle={\frac{{{1}-{{\sin}^{{2}}\theta}}}{{{\sin{\theta}}}}}$$
$$\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{{\cos}^{{2}}\theta}}}{{{\sin{\theta}}}}}$$
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