If $sin\theta =\frac{8}{17}$ where θ is an acute angle, then what is the value of tan θ + cot θ ?
Answer & explanation
Correct answer: option 3
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
= \(\frac{P}{B}\) + \(\frac{B}{P}\)
= \(\frac{8}{15}\) + \(\frac{15}{8}\)
= \(\frac{289}{120}\)