Question

verify each identity for the given value of theta
[(tan theta) (csc^2 theta )]sec^2 theta = cot theta ...theta=4pi/3

Answer 1

\[(\tan \theta \csc ^{2} \theta ) \div \sec ^{2}\theta = \cot \]\[\[(\tan \theta \csc ^{2} \theta ) \div \sec ^{2}\theta = \cot \\]

Answer 2

\[(\tan \theta) (\csc^2 \theta) / (\sec^2 \theta)=\cot \theta\]\[\frac{ (\tan \theta) (\csc^2 \theta) }{ \sec^2 \theta } =\cot \theta \rightarrow \frac{ \sin \theta }{ \cos \theta } \times \frac{ 1 }{ \sin^2 \theta } \times \frac{ 1 }{ \frac{ 1 }{ \cos^2 \theta }} = \cot \theta \]\[\frac{ \sin \theta }{ \cos \theta } \times \frac{ 1 }{ \sin^2 \theta } \times \cos^2 \theta= \cot \theta \rightarrow \frac{ \cancel{\sin \theta} }{ \cancel{\cos \theta} } \times \frac{ 1 }{ \cancel{(\sin \theta)} (\sin \theta) } \times \cancel{(\cos \theta)}(\cos \theta)= \cot \theta\]\[\frac{ \cos \theta }{ \sin \theta }= \cot \theta \rightarrow \cot \theta = \cot \theta \rightarrow \cot \left( \frac{ 4 \pi }{ 3 } \right) = \cot \left( \frac{ 4 \pi }{ 3 } \right) \implies R.S = L.S\]
@soapia