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

Wotzdorfg 2021-09-16 Answered
Verify the identity \(\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{{\cos}^{{2}}\theta}}}{{{\sin{\theta}}}}}\)

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Pohanginah
Answered 2021-09-17 Author has 22550 answers
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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Answered 2021-12-11 Author has 11829 answers

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