Math, asked by 19xbrsristii, 3 months ago

Please solve this without using the trigonometric table

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Answered by Anonymous
21

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}}

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