Question

If cosec theta / sin theta - x/ tan ² theta= 1 find the value of x easy

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

•GiVeN

$\bf\red{\frac{cosec\theta}{sin\theta} -\frac{x}{tan{}^{2}\theta}=1}$

•TO FinD

$x=?$

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$\huge\star {\underline{Solution}}$

$\implies\bf\red{\frac{cosec\theta}{sin\theta} -\frac{x}{tan{}^{2}\theta=1}}$ $\implies \bf\frac{1}{sin{}^{2}\theta} -\frac{x}{\frac{sin{}^{2}\theta}{cos{}^{2}\theta}}=1$

$\implies\bf\frac{1}{sin{}^{2}\theta} -\frac{x\:cos{}^{2}\theta}{sin{}^{2}\theta}=1$

$\implies \bf \frac{1-xcos{}^{2}\theta}{sin{}^{2}\theta}=1\\ \implies\bf 1-xcos{}^{2}\theta=\bf sin{}^{2}\theta\\ \implies \bf 1-sin{}^{2}\theta=\bf x\:cos{}^{2}\theta\\ \implies\bf cos{}^{2}\theta=x\:cos{}^{2}\theta\\ \implies x=\frac{\cancel{cos{}^{2}\theta}}{\cancel{cos{}^{2}\theta}}\\ \implies\bf \boxed{\bf \red{x=1}}\:\:(answer)$

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•FormulA UseD

$\bf\rightarrow 1-sin{}^{2}\theta=cos{}^{2}\theta\\ \bf\rightarrow tan\theta=\frac{sin\theta}{cos\theta}\\ \bf\rightarrow cosec\theta=\frac{1}{sin{}^{2}\theta}\\ \bf\rightarrow sec\theta=\frac{1}{cos\theta}$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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