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If cos x + cos square x = 1, then sin^12 x + 3 sin^10 x + sin^6 x =

Hello student, Please find the answer to your question below

cos x + cos ^2 x = 1
cos x = 1 – cos^2 x = sin^2 x

sin^12 x + 3 sin^10 x + sin^6 x
= cos^6 x + 3cos^5 x + cos^3 x
= cos^3 x (cos^3 x + 3cos^2 x +1 )
Now use can further use, cos x = 1 – cos^2 x = sin^2 x
and simplify it further