Question

if tanB=3/4

then show that
3sin2B + 4cos2B =4

Answer 1

tanB = 3/4

sinB = 3/5
cosB = 4/5
(Draw a 3-4-5 right triangle to see this)

Now recall your double-angle formulas:
sin2B = 2 sinB cosB
cos2B = cos^2B - sin^2B

Now just plug in your numbers...