Question

if sinθ =20/29 and θ is acute then find the value of 3sinθ+4cosθ/3sinθ-4cosθ

Answer 1

sin Ф = 20/29
cos Ф = 21/29

3sinФ+(4cosФ/3sinФ)-4cosФ=

3(20/29)+[4(21/29)/3(20/29]-4(21/29)=
(60/29)+[84/60]-(84/29)=
2.0689655172+1.4-2.8965517241=
3.4689655172-2.8965517241=

0.5724137931 =  answer 

Answer 2

from Pythagorean theorem we get adjacent=21
then cosθ = 21/29
3sinθ+4cosθ/3sinθ-4cosθ=3[20/29]+4[21/29]/3[20/29]-4[21/29]=(60/29+84/29)/60/29-84/29=-16