question_answer

Simplify: \[\frac{\mathbf{3 sin 67{}^\circ }}{\mathbf{5 cos 23{}^\circ }}\mathbf{+}\frac{\mathbf{5}}{\mathbf{2}}\frac{\mathbf{Sec39{}^\circ }\mathbf{.cos51{}^\circ }}{\mathbf{(1+co}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{ 51)}}\mathbf{+}\frac{\mathbf{8}}{\mathbf{9}}\]\[\mathbf{(cose}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{42{}^\circ }-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{48{}^\circ )}\]

A)  \[3\frac{89}{90}\]        

B)  \[2\frac{81}{90}\]

C)  \[cos\text{ }67{}^\text{o}+\,sec\text{ }39{}^\text{o}\]

D) \[\frac{3}{5}\cos 67{}^\circ +\frac{5}{2}\sec 51{}^\circ +\frac{8}{9}{{\cot }^{2}}\text{48}{}^\circ \]

E) None of these