Question

Tan^2 theta /1+tan^2 theta + cot^2 theta/1+cot^2 theta =1

Answer 1

Explanation:

Properties used :

1 + (tan z)^2 = (sec z)^2 = 1/(cos z)^2

1 + (cot z)^2 = (cosec z)^2 = 1/(sin z)^2

(sin z)^2 + (cos z)^2 = 1

Taking LHS

={(tan z)^2/1+(tan z)^2} + {(cot z)^2/1+(cot z)^2}

={(tan z)^2/(sec z)^2} +

{(cot z)^2/(cosec z)^2}

={(tan z)^2 × (cos z)^2} +

{(cot z)^2 × (sin z)^2}

={(sin z)^2} + {(cos z)^2} = 1 = RHS

Hence, proved.