Question

Given : $sin\Theta =\frac{p}{q}$,
$cos\Theta +sin\Theta$ in terms of p and q is $\frac{p+\sqrt{q^2+p^2}}{q}$
if true then write 1 and if false then write 0

Answer 1

$\sin \Theta =\frac{p}{q}$
$\sin \Theta =\frac{P}{H}=\frac{p}{q}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$q^2=p^2+B^2$
$B=\sqrt{q^2-p^2}$
Now, $\cos \Theta +\sin \Theta$
= $\frac{B}{H}+\frac{P}{H}$
= $\frac{\sqrt{q^2-p^2}}{q}+\frac{p}{q}$
= $\frac{p+\sqrt{q^2-p^2}}{q}$