The value of $\frac{3tan^260°+sec^230°-sin^245°}{(cos15°+sin75°)(sec15°+cosec75°)}$ is :

$\frac{5}{12}$ $\frac{65}{24}$ $\frac{13}{12}$ $\frac{59}{24}$

$\frac{59}{24}$

$\frac{3tan^260°+sec^230°-sin^245°}{(cos15°+sin75°)(sec15°+cosec75°)}$ { using , sinA = cos ( 90° - A ) } = $\frac{3 ×(√3)²+(2/√3)² - (1/√2)²}{(cos15°+cos15°)(sec15°+sec15°)}$ = $\frac{9+4/3 - 1/2}{(2cos15°)(2sec15°)}$ = $\frac{(54+8 - 3 )}{6}$ = $\frac{(59 )}{24}$