Using sec(x), cosec(x), and cot(x)
\(\DeclareMathOperator{cosec}{cosec}\)
Show that \(\frac{\cot x \sec x}{\cosec^2 x}=\sin x\)
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\[\text{LHS}= \frac{\cot x \sec x}{\cosec^2 x}=\frac{\frac{\cos x}{\sin x}\frac{1}{\cos x}}{\frac{1}{\sin^2x}}\]
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\[= \frac{\frac{1}{\sin x}}{\frac{1}{\sin^2 x}}\]
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\[=\frac{1}{\sin x}\times \frac{\sin^2x}{1}\]
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\[=\frac{\sin^2x}{\sin x}\]
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\[=\sin x\]
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\[=\text{RHS}\]
Solve \(\sec x = \sqrt{ 2 }\) in the interval \(0\leq x\leq2\pi\)
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\[\cos x=\frac{1}{\sqrt{ 2 }}\]
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\[x=\frac{\pi}{4}\]
- \(\(x=\frac{7\pi}{4}\)\)
Using cast circle ^