Question

If tan Q + cot Q = 4 then tan⁴Q + cot⁴Q =

Answer 1

Answer:

$\red { Value \: of \: tan^{4} Q + cot^{4} Q}\green {= 194 }$

Step-by-step explanation:

$Given \: tan \:Q + cot\:Q = 4 \:--(1)$

/* On squaring both sides, we get

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

$\implies tan^{2} Q + cot^{2} Q+ 2tanQcotQ = 16$

$\implies tan^{2} Q + cot^{2} Q+ 2 = 16$

$\boxed { \pink { tanQcotQ = 1 }}$

$\implies tan^{2} Q + cot^{2} Q = 16 - 2$

$\implies tan^{2} Q + cot^{2} Q = 14 \: ---(2)$

\* On squaring both sides, we get

$\implies( tan^{2} Q + cot^{2} Q)^{2} = 14^{2}$

$\implies tan^{4} Q + cot^{4} Q+ 2tan^{2}Qcot^{2}Q = 196$

$\implies tan^{4} Q + cot^{4} Q+ 2= 196$

$\implies tan^{4} Q + cot^{4} Q= 196-2\\= 194$

Therefore.,

$\red { Value \: of \: tan^{4} Q + cot^{4} Q}\green {= 194 }$

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