Evaluate the following expression.

$\frac{tan^260°+cosec30°sin90°+3sec^230°}{4sin^245°+sec^260°-cot^230°-5cos^290°}$

3

$\frac{tan^260°+cosec30°sin90°+3sec^230°}{4sin^245°+sec^260°-cot^230°-5cos^290°}$

= \(\frac{ (√3)² + 2 × 1 + 3×( 2/√3)² }{ 4× (1/√2)² + 2² - (√3)² - 5 × 0 }\)

= \(\frac{ 3 + 2 × 1 + 4 }{ 2+ 4 - 3 -0 }\)

= \(\frac{ 9 }{ 3 }\)

= 3