Question

3tan theta =4 show that 3sin theta +2 cos theta / 3sin theta -2 cos theta =3
​

Answer 1

Step-by-step explanation:

3tan θ=4

tan θ=4/3

p=4,b=3

h=√p²+b²=√4²+3²=√16+9=√25=5

sin θ=p/h=4/5

cos θ=b/h=3/5

LHS

3sinθ+2cosθ/3sinθ-2cosθ

=(3×4/5+2×3/5)/(3×4/5-2×3/5)

=(12/5+6/5)/(12/5-6/5)

=(18/5)/(6/5)

=18/5×5/6

=3

LHS=RHS

HENCE PROVED