If $sin\theta =\frac{8}{17}$ where θ is an acute angle, then what is the value of tan θ + cot θ ?

$\frac{217}{110}$ $\frac{281}{190}$ $\frac{289}{120}$ $\frac{512}{321}$

$\frac{289}{120}$

We are given that :- sin θ = \(\frac{8}{17}\) { we know, sinθ = \(\frac{P}{H}\) } By using pythagoras theorem, P² + B² = H² 8² + B² = 17² B = 15 Now, tan θ + cot θ = \(\frac{P}{B}\) + \(\frac{B}{P}\) = \(\frac{8}{15}\) + \(\frac{15}{8}\) = \(\frac{289}{120}\)