Question

if theta is an acute angle and tan theta + cot theta = 2, find the value of tan^12 theta + cot^12 theta ​

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

$Given \: \theta\:is \:an \:acute \:angle .$

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

$\implies tan \theta+ \frac{1}{tan\theta} =2$

$\implies \frac{tan^{2} \theta + 1}{tan\theta } = 2$

$\implies tan^{2} \theta + 1 = 2tan\theta$

$\implies tan^{2} \theta + 1 -2tan\theta=0$

$\implies tan^{2} \theta + 1^{2} - 2tan\theta\times 1=0$

$\implies ( tan\theta - 1)^{2} = 0$

$\implies tan\theta - 1 = 0$

$\implies tan \theta = 1\: ---(2)$

$Now, \:Value \: of \:tan^{12} \theta + cot^{12} \theta \\= (tan \theta)^{12} + \frac{1}{(tan\theta)^{12}} \\= 1 + 1 \: [ From \: (2) ] \\= 2$

Therefore.,

$\red { Value \:of \:tan^{12} \theta + cot^{12} \theta }\green { = 2 }$

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