Question

tan 0 / 1 - cot 0 + cot 0 / 1 - tan 0
= 1 + sec cosec
[Hint : Write the expression in terms of sine and cos 0]​

Answer 1

$LHS = \frac{tan 0}{1-cot 0} + \frac{cot 0}{ 1 - tan 0 }$

$= \frac{\frac{sin 0}{cos 0}}{1 - \frac{cos 0}{sin 0}} + \frac{\frac{cos 0 }{sin 0}}{1 - \frac{sin 0}{cos 0}}$

$= \frac{sin^{2} 0}{cos 0(sin 0 - cos 0)} + \frac{ cos^{2} 0}{ sin 0(cos 0 - sin 0) }$

$= \frac{sin^{2} 0}{cos 0(sin 0 - cos 0)} - \frac{ cos^{2} 0}{ sin 0 (sin 0 - cos 0) }$

$= \frac{sin^{3} 0 - cos^{3} 0}{ sin 0 cos 0 (sin 0 - cos 0) }$

$= \frac{ (sin 0 - cos 0) ( sin^{2} 0 + sin 0 cos 0 + cos^{2} 0 ) }{ sin 0 cos 0 ( sin 0 - cos 0)}$

$= \frac{ 1+sin 0 cos 0 }{ sin 0 cos 0 }$

$= \frac{1}{sin 0 cos 0 } + \frac{sin 0 cos 0}{sin 0 cos 0 }$

$= Cosec 0 sec 0 + 1$

$= RHS$

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Answer 2

Step-by-step explanation:

solution starts from 1st page