If cosecθ = 0.75

find the value of  \(\frac{8tanθ - 5cosθ+1}{ 3cosecθ + 4tanθ-1}\) + \(\frac{10}{11}\).

\(\frac{103}{77}\)

cosecθ = \(\frac{125}{75}\) = \(\frac{5}{3}\) = \(\frac{H}{P}\) (Triplet 3, 4, 5)

B = 4

Put than and find

⇒ \(\frac{8×\frac{3}{4}-5×\frac{4}{5}+1}{3\frac{5}{3}+4×\frac{3}{4}-1}\) + \(\frac{10}{11}\)

⇒ \(\frac{6 - 4 + 1 }{5 + 3 -1}\) + \(\frac{10}{11}\)

⇒ \(\frac{3}{7}\) +\(\frac{10}{11}\)

= \(\frac{33 + 70}{77}\)  = \(\frac{103}{77}\)