Question

If $tan\theta +cot\theta =2$, find the value of $ta{n}^2\theta +co{t}^2\theta$

Answer 1

We have,

$tan\theta +cot\theta =2$

$(tan\theta +cot\theta {)}^2=4$

$ta{n}^2\theta +co{t}^2\theta +2tan\theta cot\theta =4$ (on squaring both sides)

$ta{n}^2\theta +co{t}^2\theta +2=4$ (because $tan\theta cot\theta =1$)

$ta{n}^2\theta +co{t}^2\theta =2$