Question

सिद्ध कीजिए कि tanA/(1 – cot A) + cotA/(1 – tanA) = 1 + secA. cosecA

Answer 1

Answer:

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Answer 2

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

tanA/(1 – cot A) + cotA/(1 – tanA) = 1 + secA. cosecA

Formula To be used :-----

• CotA = 1/TanA
• (a³-b³) = (a-b)(a²+b²+ab)
• cotA = cosA/sinA
• tanA = sinA/cosA
• sin²A+cos²A = 1

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See my solution in easiest way :--------

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$\frac{ \tan(a) }{1 - cot(a) } + \: \frac{cot(a)}{1 - \tan(a) } \\ \\ \\ \\ \frac{ \tan(a) }{1 - \frac{1}{ \tan(a) } } + \frac{ \frac{1}{ \tan(a) } }{1 - \tan(a) } \\ \\ \frac{ \tan^{2}(a ) }{ \tan(a) - 1 } - \frac{1}{ \tan(a)( \tan(a) - 1) } \\ \\ \frac{ \tan^{3} (a) - 1}{\tan(a)( \tan(a) - 1)} \\ \\ \frac{ \cancel{( \tan(a) - 1)}(tan^{2}(a) + \tan(a) + 1) }{\tan(a) \cancel{( \tan(a) - 1)}} \\ \\ \frac{tan^{2}(a)}{ \tan(a) } + \frac{ \tan(a) }{ \tan(a) } + \frac{1}{ \tan(a) } \\ \\ \tan(a) + cot(a) + 1 \\ \\ (\frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) } ) + 1 \\ \\ (\frac{\sin^{2} (a) + {cos}^{2} (a) }{ \sin(a) \times \cos(a) } ) + 1 \\ \\ 1 + \sec(a) \csc(a)$

$\red{\bold{\underline{\underline{LHS=RHS}}}}$

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