Question

sin^2 30 + cos^2 30 + tan^2 30​

Answer 1

Thanks for your question ...

Your required answer :

===> 4/3

Given :

• sin²30° + cos²30° + tan²30°

Values :

• sin²30° - 1/2
• cos²30° - √3/2
• tan²30° - 1/√3

Now Solution :

$= (\frac{1}{2}) {}^{2} + (\frac{ \sqrt{3} }{2}) {}^{2} + (\frac{1}{ \sqrt{3} }) {}^{2} \\ \\ = \frac{1}{4} + \frac{3}{4} + \frac{1}{3} \\ \\ = \frac{3 + 9 + 4}{12} \\ \\ = \frac{16}{12} \\ \\ = \frac{4}{3} \\ \\ \red{Brainliest \: Please}$

Answer 2

$\sf \fbox \red{ \underline{Solution}}$

$\sf \: :⟹we \: know \: that \:$

$\sf \: :⟹ \sin(30) = \frac{1}{2}$

$\sf \: :⟹ \cos(30) = \frac{ \sqrt{3} }{2}$

$\sf \: :⟹ \tan(30) = \frac{1}{ \sqrt{3} }$

$\rule{190pt}{2pt}$

$\sf \: :⟹we \: have \: to \: find \: the \: value \: of \: \\ \sf{ \sin(30) }^{2} + { \cos(30) }^{2} + { \tan(30) }^{2}$

$\rule{190pt}{2pt}$

$\sf \: :⟹now$

$\sf \: :⟹ {sin}^{2} 30 + \cos ^{2}30 + { \tan}^{2} 30 \\ \\ \sf \: :⟹ {( \frac{1}{2}) }^{2} + {( \frac{ \sqrt{3} }{2} )}^{2} + {( \frac{1}{ \sqrt{3} } )}^{2} \\ \\ \sf \: :⟹ \frac{3 + 9 + 4}{12} \\ \\ \sf \: :⟹ \frac{16}{12} \\ \\ :⟹ \frac{4}{3}$

$\rule{190pt}{2pt}$

$\sf \:answer :⟹ \rm \:\boxed{ \rm{ \frac{4}{3} }}$