If θ is positive acute angle and 3 (sec²θ + tan²θ ) = 5, then which one is true ?

$3left(sec ^{2} heta+ an ^{2} heta ight)=5$

$Rightarrow 3left(1+ an ^{2} heta+ an ^{2} heta ight)=5$

$Rightarrow 3+6 an ^{2} heta=5$

$Rightarrow 6 an ^{2} heta=5-3=2$

$Rightarrow an ^{2} heta=frac{2}{6}=frac{1}{3} quad herefore an heta=frac{1}{sqrt{3}}= an 30^{circ}$

$Rightarrow heta=30^{circ}$

$cos 2 heta=cos 60^{circ}=frac{1}{2}$

$sin heta=sin 30^{circ}=frac{1}{2}$