If sinA+sin^2+sin^3=1 prove that     cos^6A-4cos^4A+8cos^2A=4

Please answer in a simpler way than the book

Asked by guptaabhinav0809 | 10th Feb, 2019, 11:47: PM

Expert Answer:

sinA space plus space sin squared straight A plus sin cubed straight A equals 1
sinA space plus 1 minus space cos squared straight A plus sin cubed straight A equals 1.............. left parenthesis sin squared straight A equals 1 minus space cos squared straight A right parenthesis
sinA plus sin cubed straight A equals cos squared straight A
squaring
open parentheses sinA plus sin cubed straight A close parentheses squared equals cos to the power of 4 straight A
sin squared straight A plus 2 sin to the power of 4 straight A plus sin to the power of 6 straight A equals cos to the power of 4 straight A
1 minus cos squared straight A plus 2 open parentheses sin squared straight A close parentheses squared plus open parentheses sin squared straight A close parentheses cubed equals cos to the power of 4 straight A
1 minus cos squared straight A plus 2 open parentheses 1 minus space cos squared straight A close parentheses squared plus open parentheses 1 minus space cos squared straight A close parentheses cubed equals cos to the power of 4 straight A

using space left parenthesis straight a minus straight b right parenthesis squared equals straight a squared minus 2 ab plus straight b squared space and space open parentheses straight a minus straight b close parentheses cubed equals straight a cubed minus 3 straight a squared straight b plus 3 ab squared minus straight b cubed

1 minus cos squared straight A plus 2 open parentheses 1 minus 2 cos squared straight A plus space cos to the power of 4 straight A close parentheses plus open parentheses 1 minus 3 cos squared straight A plus 3 cos to the power of 4 straight A minus space cos to the power of 6 straight A close parentheses equals cos to the power of 4 straight A
4 minus 8 cos squared straight A plus 4 cos to the power of 4 straight A minus cos to the power of 6 straight A equals 0
4 equals 8 cos squared straight A minus 4 cos to the power of 4 straight A plus cos to the power of 6 straight A

Answered by Arun | 11th Feb, 2019, 10:03: AM