Question

if 3tan tita=4,show that( 4cos tita-sin tita/2cos tita+sin tita)=4/5

Answer 1

I assume you mean:

(4cosØ - sinØ)/(2cosØ+sinØ) = 4/5
the way you typed it, the statement would be false.

given: tanØ = 4/3
make a sketch of the right-angled triangle.
You should recognize the 3-4-5 right-angled triangle, if not
r^2 = 3^2 + 4^2 = 25
r = 5
then sinØ = 4/5 and cosØ = 3/5

LS = ((4(3/5) - 4/5)/(2(3/5) + 4/5)
= (8/5) / (10/5)
= (8/5)(5/1)
= 4/5
= RS