Question

If tan A + cot A = 4, then write the value of tan⁴ A + cot⁴ A.

Answer 1

$$\begin{gathered} \tan A+\cot A=4 \\ \mathrm{Squaring}\mathrm{both}\mathrm{the}\mathrm{sides}: \\ {\tan }^{2}A+co{t}^{2}A+2=16 \\ \Rightarrow {\tan }^{2}A+co{t}^{2}A=14 \\ \mathrm{Squaring}\mathrm{both}\mathrm{the}\mathrm{sides}\mathrm{again}: \\ {\tan }^{4}A+co{t}^{4}A+2=196 \\ \Rightarrow {\tan }^{4}A+co{t}^{4}A=194 \end{gathered}$$