Question

if tan theta + cot theta =2 prove that tan2 theta + cot2 theta = 2​

Answer 1

$Given \: tan \theta + cot \theta = 2 \: --(1)$

/* On squaring both sides of the equation,we get*/

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

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

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

$\boxed{\pink { tan \theta cot \theta = 1 }}$

$\implies tan^{2} \theta + cot^{2} \theta = 4-2$

$\implies \green {tan^{2} \theta + cot^{2} \theta = 2}$

$Hence\: Proved$

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