Question

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

 

Answer 1

\[\tan A + \cot A = 4\]
Squaring both the sides: 
\[ \tan^2 A + co t^2 A + 2 = 16\]
\[ \Rightarrow \tan^2 A + co t^2 A = 14\]
Squaring both the sides again: 
\[ \tan^4 A + co t^4 A + 2 = 196\]
\[ \Rightarrow \tan^4 A + co t^4 A = 194\]