Question

plz solve this plz ............

Answer 1

$\boxed{\boxed{\mathbf{i) \:\: 0  \:\:\:\: ; \quad ii) \: \: \frac{\sqrt3}{2}}}}$

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$\large\underline{\mathsf{Finding \: the \: Value \: of \: \theta}}$

$\cot^2 \theta - 3 = 0\\=> \cot^2 \theta = 3\\=> \cot \theta = \sqrt 3\\\\For\: \theta = 30, The \:Value \: of \: \cot \theta = \sqrt3\\\\Hence, \boxed{ \theta = 30}$

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Now,

$\mathsf{ i) \cos 3 \theta = \cos 3(30) = \boxed{ \cos 90 = 0}}\\ \\\mathsf{ ii) \sin 2 \theta = \sin 2 (30) = \boxed{\sin 60 = \frac{\sqrt3}{2}}}$

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