Question

$\cos(a) - \sin(a) + 1 \div \cos(a) + \sin(a) - 1 = cosec(a) + \cot(a) . \\ using \: the \: identity \: {cosec}^{2} (a) = 1 + {cot}^{2} (a)$
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Answer 1

Answer:

LHS :

$\sf :\implies \dfrac{\cos(a) - \sin(a) + 1}{ \cos(a) + \sin(a) - 1}$

$\sf :\implies \dfrac{\cos(a) - \sin(a) + 1 }{\dfrac{\sin(a) }{ \dfrac{\cos(a) + \sin(a) - 1}{ \sin(a) }}} \qquad\Bigg\lgroup\textsf{\textbf{Dividing the Numerator and Denominator by \sin (a)}}\Bigg\rgroup$

$\sf :\implies \dfrac{\cot(a) - 1 + \cosec(a)}{ \cot(a) +1 - \cosec(a)}$

$\sf :\implies\dfrac{\cot(a)+ \cosec(a) - \bigg\{\cosec^{2} (a) - \cot^{2} (a) \bigg\}}{ \cot(a) +1 - \cosec(a)}$

$\sf :\implies\dfrac{\cot(a)+ \cosec(a) - \bigg\{\cosec (a) + \cot(a) \bigg\}\bigg\{\cosec (a) - \cot(a) \bigg\}}{ \cot(a) +1 - \cosec(a)}$

$\sf :\implies\dfrac{\cot(a)+ \cosec(a) - \bigg\{1 - \cosec(a) - \cot(a) \bigg\}}{ \cot(a) +1 - \cosec(a)} \qquad\Bigg\lgroup\textsf{\textbf{Taking \cot (a) and \cosec (a) common}}\Bigg\rgroup$

$\sf :\implies\cot(a) + \cosec(a)$

= RHS

Answer 2

Answer:

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A drinking glass is in the shape of a frustum of a cone height 14 cm . the diameters of its two circular ends are 4 cm and 2 cm . find the capacity of the glass.

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