Question

(Tan A ÷1_cotA) + (cotA÷1_tanA) =?

Answer 1

Hi ,

tan A / ( 1 - cot A ) + cot A/ ( 1 - tan A )

= tan A / [1 -(1/ tan A )] + ( 1/tanA ) / ( 1 - tan A )

= tan² A /(tan A - 1 ) - 1/ [ tan A (tan A - 1 ) ]

= ( tan³ A - 1 ) / [ tan A ( tan A - 1 ) ]

= ( tan A - 1 ) [ 1 - tan A - tan² A ]/[tan A (tanA-1)]

= ( 1 + tan² A - tanA ) / tanA

= ( sec² A - tanA ) / tanA

= ( sec² A / tanA ) - 1

= ( 1/sinA cosA ) - 1

= cosecAsecA - 1

I hope this helps you.

:)