Question

10
5 cos 260° +4sec 230° - tan230°
Sin 230° + cos2 30°​

Answer 1

$\longrightarrow \sf \dfrac{5 { \cos}^{2}60 + 4{ \sec}^{2}30 - { \tan}^{2}30}{ { \sin}^{2} 30 + { \cos}^{2}30} \\ \\\longrightarrow \sf \dfrac{5 { \bigg( \dfrac{1}{2} \bigg)}^{2} + 4{ \bigg( \dfrac{2 }{ \sqrt{3} }\bigg) }^{2} - {\bigg( \dfrac{1}{ \sqrt{3} }\bigg )}^{2}}{ {\bigg ( \dfrac{1}{2}\bigg) }^{2} + { \bigg( \dfrac{ \sqrt{3} }{2}\bigg) }^{2}} \\ \\\longrightarrow \sf \dfrac{5 \times \dfrac{1}{4} + 4 \times \dfrac{4}{3} - \dfrac{1}{3}}{ \dfrac{1}{4} + \dfrac{3}{4} } \\ \\ \longrightarrow \sf \dfrac{ \frac{5}{4} + \dfrac{16}{3} - \dfrac{1}{3} }{ \dfrac{1}{4} + \dfrac{3}{4} } \\ \\ \longrightarrow \sf \dfrac{ \dfrac{15 + 64 - 4}{12} }{ \dfrac{1 + 3}{4} } \\ \\ \longrightarrow \sf \dfrac{ \dfrac{75}{12} }{ \dfrac{4}{4} } \\ \\\longrightarrow \sf \dfrac{75}{12}\\ \\ \longrightarrow \sf \dfrac{25}{4}$