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4. Prove that sin^2 (8x) - …

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4. Prove that sin^2 (8x) - sin^2 (3x) =sin 11x.sin 5x 04 1

Posted by Aditya Thakur 1 year, 5 months ago

CBSE > Class 11 > Mathematics

3 answers

Shivam Jha 1 year, 5 months ago

As we know, Sin²x - Sin²y = Sin(x+y) Sin(x-y) Thus, Sin²8x - Sin²3x = (Sin8x + Sin3x) X (Sin8x - Sin3x) Since, Sinx + Siny = 2Sin[(x+y)/2] Cos[(x-y)/2] Sinx + Siny = 2Cos[(x+y)/2] Sin[(x-y)/2] (2Sin11x/2 X Cos5x/2) X (2Cos11x/2 X Sin5x/2) (2 Sin11x/2 X Cos11x/2) X (2 Sin5x/2 X Cos5x/2) Sin11x X Sin5x H.P! {2SinxCosx = Sin2x}

ᥫ᭡ㅤᏒᴀᴜsʜꫝɴ .. 1 year, 5 months ago

There's a mistake done by me.. Sin(8x+3x).Sin(8x-3x) = sin11x.sin5x

ᥫ᭡ㅤᏒᴀᴜsʜꫝɴ .. 1 year, 5 months ago

As we knw that, sin²x - sin²y = sin(x+y)sin(x-y) Therefore, Sin² 8x - Sin² 3x = Sin (8x+3x). × Sin(8x-3x) Sin11x.sin5x Hence LHS=RHS (proved)

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