Question

(Tanx+cotx)^2=cosec^2x+sec^2x

Answer 1

Answer:

LHS = RHS.

Step-by-step explanation:

${( \tan( \alpha ) + \cot( \alpha )) }^{2} = { \tan( \alpha ) }^{2} + { \cot( \alpha ) }^{2} + 2 \tan( \alpha ) \cot( \alpha ) \\ \\ = { \sec( \alpha ) }^{2} - 1 + { \csc( \alpha ) }^{2} - 1 + 2 \\ \\ = { \csc( \alpha ) }^{2} + { \sec( \alpha ) }^{2} . \\ \\ = rhs \\ \\ hence \: \: proved.$