Question

sin theta is equal to P divided by Q find cos theta + sin theta in terms of P and Q

Answer 1

HELLO......FRIEND!!

THE ANSWER IS HERE,


I take theta as a. For my convenience .

$= > \: \sin( a) = \frac{p}{q}$

$= > \: \sin( a ) + \cos(a)$

$= > \: \sin(a) + \sqrt{1 - ( { \sin(a) })^{2} }$

$= > \: \frac{p}{q} + \sqrt{1 - \frac{ {p}^{2} }{ {q}^{2} } }$

$= > \: \frac{p}{q} + \sqrt{ \frac{ {q}^{2} - {p}^{2} }{ {q}^{2} } }$

$= > \: \frac{p + \sqrt{ {q}^{2} - {p}^{2} } }{q}$

:-)Hope it helps u.

Answer 2

Hi Friend !!!

====================

let theta be @ (for representation)

$sin \alpha = \frac{p}{q} \\ \\ sin \alpha + \cos( \alpha ) \\ \\ = > \sin( \alpha ) + \sqrt{1 - { \ \sin( \alpha ) }^{2} } \\ \\ = > \frac{p}{q} + \sqrt{1 - (\frac{p}{q} )^{2} } \\ \\ = > \frac{p}{q} + \sqrt{ \frac{ {q}^{2} + {p}^{2} } { {q}^{2} } } \\ \\ = > \frac{p + \sqrt{ q^{2} + {p}^{2} } }{q}$
Hope it helps u