If $cosec \theta = 1.25,$ then $\frac{4 \tan \theta - 5 \cos \theta + 1}{\sec \theta + 4 \cot \theta -1} = ?$
Answer & explanation
Correct answer: option 2
cosecθ = 1.25
cosecθ = \(\frac{5}{4}\)
{ we know that ,cosecθ = \(\frac{H}{P}\) }
By using pythagoras theorem ,
P² + B² = H²
4² + B² = 5²
B² = 25 - 16
B² = 9
B = 3
Now,
\(\frac{4tanθ - 5cosθ + 1 }{secθ +4 cotθ - 1 }\)
= \(\frac{4 × 4/3 - 5 × 3/5 + 1 }{5/3 + 4×3/4 - 1 }\)
= \(\frac{16/3 - 3 + 1 }{5/3 + 3 - 1 }\)
= \(\frac{10 }{11 }\)