Question

tan theta-cot theta =1 then tan²theta +cot²theta

Answer 1

Hey mate here is your answer-------
tan theta-cot theta =1

or,(tan theta-cot theta)^2=1^2

or,tan^2 theta+cot^2 theta-2tan theta×cot theta=1

or,tan^2 theta+cot^2 theta-2=1

or,tan^2 theta+cot^2 theta=3[ans.]

Hope it will help you

Answer 2

given

$tan \theta - cot \theta = 1$

we have to find tan²θ+cot²θ

Now

$(tan \theta - cot \theta) ^{2} = 1 \\ \\ {tan}^{2} \theta + {cot}^{2} \theta - 2 tan \theta cot \theta= 1 \\ \\ {tan}^{2} \theta + {cot}^{2} \theta - 2 = 1$

${tan}^{2} \theta + {cot}^{2} \theta = 3$