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If (cos^2 x)/a = (sin^2 x)/b, then (cos^4 x)/a + (sin^4 x)/b =

If (cos^2 x)/a = (sin^2 x)/b, then (cos^4 x)/a + (sin^4 x)/b =

Grade:11

1 Answers

sonika p
129 Points
4 years ago
given, (cos^2 x)/a = (sin^2 x)/b 
b(cos^2 x) – a(sin^2 x) = 0
b(1 – (sin^2 x)) – a(sin^2 x)=0
b –b (sin^2 x) – a(sin^2 x) = 0
b – (a+b)(sin^2 x) = 0
b = (a+b) (sin^2 x).......(1)
 (cos^4 x)/a + (sin^4 x)/b
=a( ((cos^2 x)/a)^2) +b( ((sin^2 x)/a)^2)
= a( ((sin^2 x)/b)^2) +b( ((sin^2 x)/a)^2) = (a+b)((sin^2 x)/b)^2
from equation (1),
(a+b)*(1/(a+b)^2) = 1/(a+b)

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