Question

if 4 tan they a equal to 3 evaluate (4 sin they a - cos they a plus 1 )

Answer 1

4tanθ = 3 so, tanθ = 3/4
We know, tanθ = perpendicular/base
so, Perpendicular/base = 3/4
∴ perpendicular = 3 and base = 4
∴ hypotenuse = √(3² + 4²) = 5

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

Now, (4sinθ - cosθ + 1)
= (4 × 3/5 - 4/5 + 1)
= (4 × 0.6 - 0.8 + 1)
= 2.4 - 0.8 + 1
= 2.6