Question

if tanA+cotA=5 show that tan^4A+cot^4A=527

Answer 1

Answer:-

tanA+cotA=5

Squaring both sides,

(tanA+cotA)^2=25

tan^2 A+cot^2 A+2tanAcotA=25

tan^2 A+cot^2 A+2=25

tan^2 A+cot^2 A=25-2=23

(tan^2 A+cot^2 A)^2=23^2

tan^4 A+cot^4 A+2tan^2A×cot^2A=529

tan^4 A+cot^4 A+2=529

tan^4 A+cot^4 A=529-2=527

Therefore, tan^4 A+cot^4 A=527

Answer 2

$tanA + cotA = 5 \\ \\ :\implies ( {tanA + cotA})^{2} = 25 \\ \\ :\implies {tan}^{2} A + {cot}^{2} A + 2 = 25 \\ \\ :\implies {tan}^{2} A + {cot}^{2} A = 23 \\ \\ :\implies ( { {tan}^{2} A + {cot}^{2}A })^{2} = 529 \\ \\ :\implies {tan}^{4} A + {cot}^{4} A + 2 = 529 \\ \\ :\implies {tan}^{4} A+ {cot}^{4} A = 527$.