If cotθ = 3/4 , θ is an acute angle, then sinθ + cosθ - tanθ is equal to:

If cotθ = 3/4 , θ is an acute angle, then sinθ + cosθ…

If cotθ = $\frac{3}{4}$ , θ is an acute angle, then sinθ + cosθ - tanθ is equal to:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac{1}{15}$ .

Pythagorean theorem: Hypotenuse² = Height² + Base²

cot θ = 3/4 = Base/Height

Hypotenuse² = 3² + 4² = 9 + 16 = 25

Hypotenuse = √25 = 5

Now, sin θ + cos θ - tan θ = (4/5) + (3/5) - (4/3) = 1/15

Therefore, the required value is 1/15.