Question

Please solve this without using the trigonometric table

Answer 1

☯ Explanation,

$\green \bigstar \: \tt \: 4 \dfrac{sin32 {}^{ \circ}}{cos58 {}^{ \circ} } + 5 \dfrac{tan48 {}^{ \circ} }{cot42{}^{ \circ} } - 8 \dfrac{sec72{}^{ \circ} }{cosec18{}^{ \circ} } \\ \\ \\ \tt : \implies \: 4 \times \dfrac{sin(90 - 32){}^{ \circ} }{cos58{}^{ \circ} } + 5 \times \dfrac{tan(90 - 48){}^{ \circ} }{cot42{}^{ \circ} } - 8 \times \dfrac{sec(90 - 72){}^{ \circ} }{cosec18 {}^{ \circ} } \\ \\ \\ \tt : \implies \: 4 \times \dfrac{cos58{}^{ \circ}}{cos58{}^{ \circ}} + 5 \times \dfrac{cot42{}^{ \circ}}{cot42{}^{ \circ}} - 8 \times \dfrac{cosec18{}^{ \circ}}{cosec18{}^{ \circ}} \\ \\ \\ : \implies \tt \: 4 \times \not\dfrac{cos58{}^{ \circ}}{cos58{}^{ \circ}} + 5 \times \not\dfrac{cot42{}^{ \circ}}{cot42{}^{ \circ}} - 8 \times \not\dfrac{cosec18{}^{ \circ}}{cosec18{}^{ \circ}} \\ \\ \\ : \implies \tt \: 4 \times 1 + 5 \times 1 +8(1) \\ \\ \\ : \implies \tt \: 4 + 5 - 8 \\ \\ \\ : \implies \tt \: 9 - 8 \\ \\ \\ : \implies \tt \underline {\boxed {\mathfrak \purple{1}} }\: \red \bigstar$

☯ Know to more,

$\bullet\:\tt Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$