0If 4 cos θ - 3 sin θ = 0 find the value of ( cos² θ • sin² θ ) / (1 + tan θ )
4 cos θ = 3 sin θ or sin θ / cos θ = 4 / 3 or. tan θ = 4 / 3 which means in the right angled triangle, opp side is 4 , adj side is 3 and hyp is 5
∴ sin θ = 4/5. cos θ = 3/5. and tan θ = 4/3
Substituting these values in the given equation ( cos ² θ • sin² θ ) / ( 1 + tan θ )
= ( 3/5 )² • ( 4/5 )² / ( 1 + 4/3 )
= ( 9/25 ) • (16/25 ) / ( 7/3 )
=( 144/625 ) / ( 7/3 )
= (144/625 ) • ( 3/7 )
= (144 • 3 )/ (625 • 7 )
= 432 / 4375
= 0.0987
