Question

if tan theta is equal to x/y find cos theta - sin theta / cos theta + sin theta​

Answer 1

When value of tanA is given say m/n,

you've : m/n = y/x.

So, y= mk & x = nk.

r = (x^2 + y^2)^1/2.

r = [ (mk)^2 + (nk)^2 ]^1/2

r = [ k^2(m^2+n^2) ]^1/2

r = k (m^2+n^2)^1/2

sinA = y/r = mk/k(m^2+n^2)^1/2

= m/(m^2+n^2)^1/2

Similarly, cosA = n/(m^2+n^2)^1/2.

Example -

tanA = 4/3

So, y= 4k & x = 3k.

r = (16k^2 + 9k^2 )^1/2 = + -5k.

sinA = + - 4/5 & cosA = + - 3/5.

Method 2 -

I explain it directly with an example.

tanA = 3/4.

sec^2A = 1 + tan^2A = 1+9/16=25/16.

secA = + - 5/4 so cosA = + - 4/5.

sinA = tanA*cosA = + - 3/5.