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Sin*4x/2 + cos*4x/3 = 1/5 show that sin*8x/8+cos*8x/27=1/125 trignometry

Sin*4x/2 + cos*4x/3 = 1/5 show that sin*8x/8+cos*8x/27=1/125 trignometry

Grade:11

1 Answers

YASH AHUJA
28 Points
6 years ago
3sin^4x +2cos^4x=6/53sin^4x +2(1-sin^2x)^2=6/53sin^4x +2sin^4x-4sin^2x+2=6/55sin^4x -4sin^2x +2=6/525sin^4x -20sin^2x+4=0(5sin^2x-2)(5sin^2x-2)=0sin^2x =2/5 , sin^8x=(2/5)^4cos^2x=1-2/5=3/5 , cos^8x=(3/5)^4Putting the values of sin^8x/8 and cos ^8x/27 we will get 1/125

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