Question

pls answer with explanation​

Answer 1

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$\longrightarrow \sf \cos \theta = \frac{ \sqrt{3} }{2} \\ \\ \longrightarrow \sf\cos \theta = \cos 30 \degree \\ \\\longrightarrow \sf \theta = 30 \degree$

Now

$\longrightarrow \sf4 { \sin}^{2} \theta + { \tan}^{2} \theta \\ \\\longrightarrow \sf 4 { \sin}^{2}30+ { \tan}^{2}30 \\ \\ \longrightarrow \sf4 \times \bigg(\frac{1}{2} {\bigg)}^{2} + {\bigg( \frac{1}{ \sqrt{3} }\bigg) }^{2} \\ \\\longrightarrow \sf 4 \times \frac{1}{4} + \frac{1}{3} \\ \\ \longrightarrow \sf1 + \frac{1}{3} \\ \\\longrightarrow \sf \frac{3 + 1}{3} \\ \\ \longrightarrow \sf \frac{4}{3}$

Option ( d ) is correct