Question

$\text{If}tan\theta +cot\theta =2,$ then $ta{n}^2\theta +co{t}^2\theta$ = _____.

• A. -2
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is D

2

Given $tan\theta +cot\theta =2$

Squaring both sides we get,

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

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

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

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