1.

If (1 + sec A)/tan A = x, then x is1). cot (A/2)2). tan(A/2)3). cosec(A/2)4). sec(A/2)

Answer»

⇒ (1 + SEC A)/tanA $(= \frac{{1{\rm{}} + {\rm{}}\frac{1}{{{\rm{cosA}}}}}}{{{\rm{tanA}}}} = \frac{{1{\rm{}} + {\rm{cosA}}}}{{{\rm{sinA}}}} = \frac{{1{\rm{}} + {\rm{cosA}}}}{{\SQRT {1 - {\rm{co}}{{\rm{s}}^2}{\rm{A}}} }})$

$(\begin{ARRAY}{l} = \frac{{1{\rm{}} + {\rm{cosA}}}}{{\sqrt {\LEFT( {1{\rm{}} + {\rm{cosA}}} \right)\left( {1 - {\rm{cosA}}} \right)} }}\\ = \frac{{\sqrt {1{\rm{}} + {\rm{cosA}}} }}{{\sqrt {1 - {\rm{cosA}}} }} \end{array})$

 = cot(A/2)



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