Question

Prove that, √{(sec θ – 1)/(sec θ + 1)} = cosec θ - cot θ. 
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Answer 1

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

$\bf\huge{\implies\sqrt{\dfrac{secA-1}{secA+1}}}$

$\bf\huge{\implies\sqrt{\dfrac{(secA-1)^2}{(secA+1)(secA+1)}}}$

$\bf\huge{\implies\sqrt{\dfrac{(secA-1)^2}{sec^2 A-1}}}$

$\bf\huge{\implies\sqrt{\dfrac{(secA-1)^2}{tan^2 A}}}$

$\bf\huge{\implies\dfrac{secA-1}{tanA}}$        

$\bf\huge{\implies\dfrac{secA}{tanA-1/tanA}}$

$\bf\huge{\implies\dfrac{1}{cosA} / \dfrac{sinA}{cosA}- cotA}$        

$\bf\huge{\implies\dfrac{1}{sinA} - cotA}$

= CosecA - cotA

$\bf\huge\bf\huge{\boxed{\bigstar{{LHS\: = \:RHS}}}}$