Question

If cosec alfa =2, what is the value of cot^2alfa?

Answer 1

$\csc( \alpha ) = 2 - - - (given) \\ threfore \\ { \ \csc ( \alpha ) }^{2} = {2 }^{2} \\ { \csc( \alpha ) }^{2} = 4 \\ we \: know \: that \\ 1 + { \cot( \alpha ) }^{2} = { \csc( \alpha ) }^{2} - - (identity) \\ 1 + { \cot( \alpha ) }^{2} = 4 \\ { \cot( \alpha ) }^{2} = 4 - 1 \\ { \cot( \alpha ) }^{2} = 3$
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