Question

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

Answer 1

tan A+cot A = 5 , 
tan^4 A +cot^4 A =527 ( prove that )


----->(tanA+cotA)^2 = 5^2 = 25

tan^2 A + 2tanA.cotA +cot^2 A = 25

(remember cotA=1/tanA --->tanA.cotA=1) 

so tan^2 A+ (2 x 1) +cot^2 a = 25

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

& now (tan^2 A +cot^2 A)^2 = 23^2 =529

---->tan^4 A +2(tanA.cotA)^2 +cot^4 A = 529
---->tan^4 A + 2 x 1^2 +cot^4 A = 529

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

so tan^4 A +cot^4 A = 527---------------------------Answer 

Answer 2

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