Question

if sin theta = x, write the value of cot theta

Answer 1

$\textbf{Given:}$

$sin\theta=x$

$\textbf{To find:}$

$\text{The value of cot\theta }$

$\textbf{Solution:}$

$\text{We know that,}$

$\bf\,sin^2\theta+cos^2\theta=1$

$\implies\,cos^2\theta=1-sin^2\theta$

$\implies\,cos^2\theta=1-x^2$

$\implies\,cos\theta=\sqrt{1-x^2}$

$\text{Now,}$

$cot\theta$

$=\dfrac{cos\theta}{sin\theta}$

$=\dfrac{\sqrt{1-x^2}}{x}$

$\therefore\textbf{The value of \bf\,cot\,\theta is \bf\dfrac{\sqrt{1-x^2}}{x} }$

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Answer 2

$Given \: sin \theta = x \: --(1)$

$Value \: of \: cot \:theta \\= \frac{cos\theta}{sin \theta } \\= \frac{\sqrt{cos^{2} \theta}}{sin \theta}\\= \frac{ \sqrt{1 - sin^{2} \theta }}{sin \theta }$

$\blue {( By \: Trigonometric \: Identity )}$

$\boxed{ \pink { cos^{2} \theta = 1 - sin^{2} \theta }}$

$= \frac{ \sqrt{ 1 - x^{2}}}{x} \: [ From \: (1) ]$

Therefore.,

$\red { Value \: of \: cot \:theta} \green {= \frac{ \sqrt{ 1 - x^{2}}}{x} }$

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