Question

answer this question ..."."

Answer 1

sin^4/a + cos^4/b = 1/a+b

cos^4/b = (cos^2)^2/b = ( 1 - Sin^2)^2 /b

= 1 + sin^4 - 2sin^2)/b

So sin^4/a + ( 1 + sin^4 - 2sin^2)/b = 1/a +b

b sin^4 + a + a sin^4 - 2a sin^2 = ab/a+b

( b+ a) sin^4 -2 a sin^2 + a = ab/a+b

(a+b)^2 sin^4 - 2a(a+b) sin^2 + a( a+b)= ab

(( a+b ) sin^2 - a)^2 -a^2 + a( a+b)= ab

( a+b) sin^2 - a)^2 - a^2 + a^2 + ab = ab

( a+b) Sin^2 - a)^2 = 0

(a+b) sin^2 - a = 0

a+b) sin^2 = a

sin^2 = a/(a+b)

sin^8 = (sin^2)^4 = ( a^4)/( a+b)^4

cos^8 = ( cos^2)^4 = ( 1 - sin^2)^4

= ( 1 - a/( a+b))^4

= a+b - a)/ (a+b))^4

= (b/(a+b))^4

So

sin^8/a^3 + cos^8/b^3

= ( a^4) / ( a+b)^4 a^3 + b ^4/ ( a+b)^4 b^3

= a/( a+b)^4 + b/( a+b)^4

= (a+b)/(a+b)^4

= 1/( a+b)^3


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