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Question: If \(\tan A + \cot A = 4,\) then \(\tan^{4}A + \cot^{4}A\) is equal to...

If tan⁡A+cot⁡A=4,\tan A + \cot A = 4, then tan⁡4A+cot⁡4A\tan^{4}A + \cot^{4}A is equal to

A

110

B

191

C

80

D

194

Answer

194

Explanation

Solution

tan⁡A+cot⁡A=4\tan A + \cot A = 4

⇒tan⁡2A+cot⁡2A+2tan⁡Acot⁡A=16\Rightarrow \tan^{2}A + \cot^{2}A + 2\tan A\cot A = 16

⇒tan⁡2A+cot⁡2A=14⇒tan⁡4A+cot⁡4A+2=196\Rightarrow \tan^{2}A + \cot^{2}A = 14 \Rightarrow \tan^{4}A + \cot^{4}A + 2 = 196

⇒tan⁡4A+cot⁡4A=194.\Rightarrow \tan^{4}A + \cot^{4}A = 194.