Question

Q) If sinA= p Find secA+tanA

Answer 1

Let angle A = x

By qn ,

$\sin(x) = p$
Next,
$\cos(x) = \sqrt{1 - { \sin(x) }^{2} }$
ie
$\cos(x) = \sqrt{1 - {p}^{2} }$
Now
$\sec(x) = \frac{1}{ \cos(x) } = \frac{1}{ \sqrt{1 - {p}^{2} } } = \frac{ \sqrt{1 + {p}^{2} } }{1 - {p}^{4} }$
and

$\tan(x) = \frac{ \sin(x) }{ \cos(x) } = \frac{p}{ \sqrt{1 - {p}^{2} } } = \frac{p \sqrt{1 + {p}^{2} } }{1 - {p}^{4} }$