Question

Given sin theta =p/q,find cos theta +sin theta in terms of p and q

Answer 1

Hope this helps u...Plz mark it as brainliest...☺

Answer 2

Given:

Sin theta=p/q

To Find:

Find cos theta + sin theta in terms of p and q

Solution:

We know that sin theta is equal to perpendicular(p) divided by hypotenuse(h) and cos theta is equal to base(b) divided by the hypotenuse(h) so by Pythagoras theorem, we can find the base to find the value of cos theta

Now finding the value of base using sin theta =p/q

$sin\theta =\frac{p}{q}$

using Pythagoras theorem

$h^2=p^2+b^2\\q^2=p^2+base^2\\base^2=q^2-p^2\\base=\sqrt{q^2-p^2}$

Now we can find the value of cos theta which will be

$cos\theta =\frac{\sqrt{q^2-p^2}}{q}$

Now finding the value of sin theta + cos theta

$=sin\theta + cos\theta\\=\frac{p}{q} +\frac{\sqrt{q^2-p^2} }{q} \\=\frac{p+\sqrt{q^2-p^2} }{q}$

Hence, the value of sin theta + cos theta in terms of p and q is $\frac{p+\sqrt{q^2-p^2} }{q}$.