If $5 \sin \theta=4$, then the value of $\frac{\sec \theta+4 \cot \theta}{4 \tan \theta-5 \cos \theta}$ is:
Answer & explanation
Correct answer: option 1
sinθ = \(\frac{4}{5}
By using pythagoras theorem ,
P² + B² = H²
4² + B² = 5²
B² = 25 - 16
B² = 9
B = 3
Now,
\(\frac{ secθ + 4cotθ }{4tanθ - 5cosθ}\)
= \(\frac{ 5/3 + 4 × 3/4 }{4× 4/3 - 5×3/5}\)
= \(\frac{ 5/3 + 3 }{16/3 - 3}\)
= \(\frac{ 14 }{7}\)
= 2