Verify the identity. csct+1/cot t = cot t/csc t-1 Choose the sequence of steps b

Question

Verify the identity. csct+1/cot t = cot t/csc t-1 Choose the sequence of steps below that verifies the identity. csc t+1/csc t = csc t + 1/cot t.csc t - 1/csc t - 1 = csc^2t/cot t(csc t - a) = cot t/csc t - 1 csc t + 1/cot t = csc t + 1/cot t.csc t - 1/csc t - 1 = csc^2 t - 1/cot t(csc t - 1) = cot^2 t/cot t(csc t - 1) = cot t/csc t - -1 csc t + 1/cot t = csc t+1/cot t.csc t + 1/csc t + 1 = csc^2t - 1/cot t(csc t - 1) = cot^2 t/cot t(csc t - 1) = cot t/csc t - 1 csc t + 1/cot t = csc t + 1/cot t = csc t + 1/cot t.csc t + 1/csc t - 1 = csc^2 t + 1/cot t(csc t - 1) = cot^2 t/cot t(csc t - 1) = cot t/csc t - 1

Explanation / Answer

( csc t + 1 ) / cot t = cot t / ( csc t -1 )

multiplying left hand side by csc t -1

( csc t + 1 ) / cot t * ( csc t -1 ) / ( csc t -1 )

= ( csc^2 t -1 ) / cot t ( csc t -1 )

csc ^2 t -1 = cot^2 t

hence, we can write

cot^2 t / cot t ( csc t -1 )

cancelling like terms from top and bottom

cot t / ( csc t -1 )

which is right side

proved !

option b is correct

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