Question

1 + tan square theta upon 1 + cot square theta is equals to 1 - tan theta upon 1 - cot theta whole square​

Answer 1

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