Correct Answer - Option 4 :
\(-\frac 1 8\)
Given:
\(\frac {\sin^2 30^\circ + \cos^2 60^\circ - \sec 35^\circ.\sin 55^\circ}{\sec 60^\circ + \rm cosec\;30^\circ}\)
Calculations:
\(\Rightarrow\frac {\sin^2 30^\circ + \cos^2 60^\circ - \sec 35^\circ.\sin 55^\circ}{\sec 60^\circ + \rm cosec\;30^\circ}\)
\(\Rightarrow\frac {(1/2)^2 + (1/2)^2 - \sec 35^\circ.\sin (90 - 55)^\circ}{2 + 2}\)
\(\Rightarrow\frac {(1/4) + (1/4) - \sec 35^\circ.\cos 35^\circ}{2 + 2}\)
\(\Rightarrow\frac {(2/4) - (1/\cos 35^\circ).\cos 35^\circ}{4}\)
\(\Rightarrow\frac {(1/2) - 1}{4}\)
\(\Rightarrow\frac {-1}{8}\)
∴ The answer is -1/8
