The value of $\frac{3cos^227°-5+3cos^263°}{tan^232°+4-cosec^258°} + sin 35°cos55° + cos35°sin55°$ is :

$\frac{1}{3}$

Using ,

sinA = cosB   Iff A + B = 90 °

secA = cosecB   Iff A + B = 90 °

$\frac{3cos^227°-5+3cos^263°}{tan^232°+4-cosec^258°} + sin 35°cos55° + cos35°sin55°$

= $\frac{3sin^263°-5+3cos^263°}{tan^232°+4-sec^232°} + sin 35°sin35° + cos35°cos35°$

= $\frac{3-5}{4-1} + 1 $

= $\frac{-2}{3} + 1 $

= $\frac{1}{3} $