===> 4/3
Given :
Values :
Now Solution :
[tex] = (\frac{1}{2}) {}^{2} + (\frac{ \sqrt{3} }{2}) {}^{2} + (\frac{1}{ \sqrt{3} }) {}^{2} \\ \\ = \frac{1}{4} + \frac{3}{4} + \frac{1}{3} \\ \\ = \frac{3 + 9 + 4}{12} \\ \\ = \frac{16}{12} \\ \\ = \frac{4}{3} \\ \\ \red{Brainliest \: Please}[/tex]
[tex] \sf \fbox \red{ \underline{Solution}}[/tex]
[tex] \sf \: :⟹we \: know \: that \: [/tex]
[tex] \sf \: :⟹ \sin(30) = \frac{1}{2} \\ [/tex]
[tex] \sf \: :⟹ \cos(30) = \frac{ \sqrt{3} }{2} \\ [/tex]
[tex] \sf \: :⟹ \tan(30) = \frac{1}{ \sqrt{3} } \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex] \sf \: :⟹we \: have \: to \: find \: the \: value \: of \: \\ \sf{ \sin(30) }^{2} + { \cos(30) }^{2} + { \tan(30) }^{2} [/tex]
[tex] \sf \: :⟹now[/tex]
[tex] \sf \: :⟹ {sin}^{2} 30 + \cos ^{2}30 + { \tan}^{2} 30 \\ \\ \sf \: :⟹ {( \frac{1}{2}) }^{2} + {( \frac{ \sqrt{3} }{2} )}^{2} + {( \frac{1}{ \sqrt{3} } )}^{2} \\ \\ \sf \: :⟹ \frac{3 + 9 + 4}{12} \\ \\ \sf \: :⟹ \frac{16}{12} \\ \\ :⟹ \frac{4}{3} [/tex]
[tex] \sf \:answer :⟹ \rm \:\boxed{ \rm{ \frac{4}{3} }} [/tex]
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===> 4/3
Given :
Values :
Now Solution :
[tex] = (\frac{1}{2}) {}^{2} + (\frac{ \sqrt{3} }{2}) {}^{2} + (\frac{1}{ \sqrt{3} }) {}^{2} \\ \\ = \frac{1}{4} + \frac{3}{4} + \frac{1}{3} \\ \\ = \frac{3 + 9 + 4}{12} \\ \\ = \frac{16}{12} \\ \\ = \frac{4}{3} \\ \\ \red{Brainliest \: Please}[/tex]
[tex] \sf \fbox \red{ \underline{Solution}}[/tex]
[tex] \sf \: :⟹we \: know \: that \: [/tex]
[tex] \sf \: :⟹ \sin(30) = \frac{1}{2} \\ [/tex]
[tex] \sf \: :⟹ \cos(30) = \frac{ \sqrt{3} }{2} \\ [/tex]
[tex] \sf \: :⟹ \tan(30) = \frac{1}{ \sqrt{3} } \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex] \sf \: :⟹we \: have \: to \: find \: the \: value \: of \: \\ \sf{ \sin(30) }^{2} + { \cos(30) }^{2} + { \tan(30) }^{2} [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex] \sf \: :⟹now[/tex]
[tex] \sf \: :⟹ {sin}^{2} 30 + \cos ^{2}30 + { \tan}^{2} 30 \\ \\ \sf \: :⟹ {( \frac{1}{2}) }^{2} + {( \frac{ \sqrt{3} }{2} )}^{2} + {( \frac{1}{ \sqrt{3} } )}^{2} \\ \\ \sf \: :⟹ \frac{3 + 9 + 4}{12} \\ \\ \sf \: :⟹ \frac{16}{12} \\ \\ :⟹ \frac{4}{3} [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex] \sf \:answer :⟹ \rm \:\boxed{ \rm{ \frac{4}{3} }} [/tex]