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If m= sin 6 x + cos 6 x, then m belongs to the interval (a) [7/8, 5/4] (b) [1/2 , 5/8] (c) [1/4, 1] Explain pls...

If m= sin6x + cos6x, then m belongs to the interval


(a) [7/8, 5/4]  (b) [1/2 , 5/8]  (c) [1/4,  1]


Explain pls...

Grade:12th Pass

1 Answers

G Narayana Raju
51 Points
9 years ago

m=sin6x+cos6x=(sin2x+cos2x)(sin4x+cos4x-sin2xcos2x)

as a3+b3=(a+b)(a2-ab+b2)

we know that,

sin2x+cos2x=1

m=((sin2x+cos2x)2-3sin2xcos2x)

m=1-3sin2xcos2x

m=1-3/4(sin2x)2

we know 0<=sin2A<=1,

so -1<=-sin22x<=0 multiply with -1,

-3/4<=-3/4(sin22x)<=0 multiply with 3/4,

1/4<=1-3/4(sin22x)<=1 add 1,

1/4<=m<=1

therefore "m" belongs to[1,1/4].

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