Question

Tan theta/ 1- cot theta + cot theta /1 - tan theta
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Answer 1

Answer:

Given,

Tan∅/ 1- cot∅ + cot∅/1 - tan∅

we write as,

sin²∅/[cos∅(sin∅-cos∅)] + cos²∅/[sin∅(cos∅-sin∅)]

=>1/(sin∅-cos∅)[sin²∅/cos∅ - cos²∅/sin∅]

=>1/(sin∅-cos∅)[(sin³∅-cos³∅)/cos∅.sin∅]

we know that

(a³-b³)= (a-b)(a²+b²+ab)

then

=> 1/(sin∅-cos∅)[(sin∅-cos∅)(sin²∅+cos²∅+sin∅.cos∅)/cos∅.sin∅]

now cancel (sin∅-cos∅) then we get

=> (sin²∅+cos²∅+sin∅.cos∅)/cos∅.sin∅

=> tan∅+cot∅+1.... (by simplification)

If you solve your copy, then you will understand well.

Answer 2

Answer:

Your answer attached in the photo