Question

1+cot^2 theta/(1+cosec theta) = cosec theta​

Answer 1

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LHS = 1 + cot^2 theta / 1 +cosec theta

1 + cosec^2 theta - 1 / cosec theta + 1

we know the trigonometric identity :

cot^2A = cosec^2A -1

1 + ( cosec theta + 1 ) ( cosec theta-1 ) / ( cosec theta + 1 )

by algebraic identity

a^2 - b^2 = ( a + b ) ( a - b )

1 + cosec theta - 1

cosec theta

RHS

1 + cot^2 theta / 1 + cosec theta = cosec theta...

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