Question

Will give brainiest!!

Answer 1

Answer:

$\frac{11}{12}$

Step-by-step explanation:

$( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \: { \bigg( \frac{ \sqrt{23} }{12} \bigg)}^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \frac{23}{144} + ( \cos \theta) ^{2} = 1 \\ \\ ( \cos \theta) ^{2} = 1 - \frac{23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{144 - 23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{121}{144} \\ \\ ( \cos \theta) = \sqrt{\frac{121}{144} } \\ \\ \cos \theta = \frac{11}{12}$