Question

if cot A =b/a,prove that 2secA+1/cos A +2 =√a^2+b^2/b
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Answer 1

Step-by-step explanation:

LHS=2secA+1/cosA+2

$= \frac{2 \times \frac{1}{cos \: a} + 1}{cos \: a + 2}$

$\frac{ \frac{2 + cos \: a}{cos \: a} }{cos \: a + 2}$

$= \frac{1}{cos \: a}$

$= \: sec \: a$

$= \sqrt{1 + cot {}^{2} a}$

$= \sqrt{1 + (\frac{ b}{a} )} {}^{2}$

$= \sqrt{ \frac{a {}^{2} + b {}^{2} }{ {a}^{2} } }$

$= \frac{ \sqrt{ {a}^{2} + {b}^{2} } }{a} = rhs$

hence proved