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Trigonometric Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
Question
If $\tan\text{A}+\cot\text{A}=4,$ then write the value of $\tan^4\text{A}+\cot^4\text{A}.$
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Answer

$(\tan\text{A}+\cot\text{A})^2=\tan^2\text{A}+\cot^2\text{A}+2\tan\text{A}\cot{A}$
$16=\tan^2\text{A}+\cot^2\text{A}+2$
$\tan^2\text{A}+\cot^2\text{A}=14$
$(\tan^2\text{A}+\cot\text{A})^4=\tan^4\text{A}+1\tan^3\text{A}\cot\text{A}6\tan^2\text{A}\cot^2\text{A}+4\tan\text{A}\cot^3\text{A}+\cot^4\text{A}$
$256=\tan^4\text{A}+4(\tan^2\text{A}+\cot^2\text{A})+\cot^4\text{A}+6$
$256=\tan^4\text{A}+4(14)+\cot^4\text{A}+6$
$\tan^4\text{A}+\cot^4\text{A}=194$

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