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if fn(x)=1/n(cos^nx +sin^nx) n=1,2,3........ then value of f4(x)-f6(x)

if fn(x)=1/n(cos^nx +sin^nx)   n=1,2,3........ then value of f4(x)-f6(x)

Grade:12th pass

1 Answers

Vishal Kumar
26 Points
3 years ago
let it be m = f4(x) - f6(x) =(1\4)(cos^4x + sin^4x) – (1\6)(cos^6x +sin^6x)         …........1
apply a^3+b^3 = (a+b)(a2+b2-a*b)
(cos2x)3 + (sin2x)3 = (sin2x + cos2x)(sin4x + cos4x – sin2x * cos2x)       ….....2 
 sin2x + cos2x = 1                                                                                               …........3
put equation 2 in equation 1
on solving upto 2-3 step 
m = 1\12 ( sin4x + cos4x  + 2 sin2x * cos2x)
judge the expression its (a + b)2
m = 1\12( sin2x + cos2x )2
again use equation 3 and get the answer 
its 1\12
 
 
 

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