Question

4tan theta =3 evaluate (4sin theta - cos theta +1)

Answer 1

4tanθ = 3 so, tanθ = 3/4

we know, tanθ = perpendicular/base
tanθ = 4/3 = perpendicular/base
So, perpendicular = 3 and base = 4
Now use Pythagoras theorem to find hypotenuse
Hypotenuse = $\bold{\sqrt{perpendicular^2+base^2}}$
∴ hypotenuse = √(3² + 4²) = √(25) = 5

Now, sinθ = perpendicular/hypotenuse = 3/5
cosθ = base/hypotenuse = 4/5

now, (4sinθ - cosθ + 1)
= 4 × 3/5 - 4/5 + 1
= 12/5 - 4/5 + 1
= 8/5 + 1
= 1.6 + 1
= 2.6

Hence, (4sinθ - cosθ + 1) = 2.6