1 + tan square theta upon 1 + cot square theta is equals to 1 - tan theta upon 1 - cot theta whole square
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Step-by-step explanation:
let theta be A
1+tan^2 A /1+cot^2 A = (1-tan A/1-cot A)^2=tan^2 A
(i) 1+tan^2 A /1+cot^2 A = tan^2 A
L.H.S
1+tan^2 A /1+cot^2 A
{ 1+tan^2 A = sec^2 A
1+cot^2 A = cosec^2 A}
1+tan^2 A /1+cot^2 A = sec^2 A/ cosec^2 A
{ sec^2 A = 1/cos^A
cosec^2 A = 1 / sin^A }
sec^2 A/ cosec^2 A = 1/cos^2 A / 1 / sin^2 A
sin^2 A /cos^2 A
= tan^2 A
(ii) (1-tan A/1-cot A)^2=tan^2 A
L.H.S
(1-tan A/1-cot A)^2
(1- sin A /cos A / 1- cos A /sin A )^2
( cos A - sin A /cos A / sin A - cos A /sin A )^2
(1 /cos A / 1 /sin A )^2
( sin A /cos A) ^2
(tan A) ^2
= tan^2 A
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