Show that the sum of 9sin^4A - 6sin^6A and 9cos^4A-6cos^6A remains constant for all values of A
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Step-by-step explanation:
R.H.S.
= cos^4A - 6cos^2Asin^2A + sin^4A
= cos^4A - 2cos^2Asin^2A + sin^4A - 4 cos^2Asin^2A
= ( cos^2A - sin^2A )^2 - ( 2cosAsinA )^2
= ( cos2A )^2 - ( sin2A )^2
= cos4A
= L.H.S
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