Question

if tan A + cot A = 4 then tan^4 A + cot^4 A is equal to

Answer 1

please find the attachment

Answer 2

$tanA + cotA = 4 \\ \\ :\implies ( {tanA + cotA})^{2} = 16 \\ \\ :\implies {tan}^{2} A + {cot}^{2} A + 2 = 16 \\ \\ :\implies {tan}^{2} A + {cot}^{2} A = 14 \\ \\ :\implies ( { {tan}^{2}A + {cot}^{2} A })^{2} = 196 \\ \\ :\implies {tan}^{4} A + {cot}^{4} A + 2 = 196 \\ \\ :\implies {tan}^{4} A + {cot}^{4} A = 194$