if sin theta plus sin squared theta plus sin cubed theta equals 1 then, prove thatcos to the power of 6 theta minus 4 cos to the power of 4 theta plus 8 c o s squared theta equals 4

Asked by pkirankumar4321 | 19th Sep, 2015, 08:37: PM

Expert Answer:

begin mathsize 14px style sin theta plus sin squared theta plus sin cubed theta equals 1 sin theta plus sin cubed theta equals 1 minus sin squared theta sin theta plus sin cubed theta equals cos squared theta S q u a r i n g space b o t h space s i d e s comma space w e space g e t left parenthesis sin theta plus sin cubed theta right parenthesis squared equals left parenthesis cos squared theta right parenthesis squared sin squared theta plus 2 sin theta sin cubed theta plus sin to the power of 6 theta equals cos to the power of 4 theta sin squared theta plus 2 sin to the power of 4 theta plus sin to the power of 6 theta equals cos to the power of 4 theta left parenthesis 1 minus cos squared theta right parenthesis plus 2 left parenthesis sin squared theta right parenthesis squared plus left parenthesis sin squared theta right parenthesis cubed equals cos to the power of 4 theta left parenthesis 1 minus cos squared theta right parenthesis plus 2 left parenthesis 1 minus cos squared theta right parenthesis squared plus left parenthesis 1 minus cos squared theta right parenthesis cubed equals cos to the power of 4 theta left parenthesis 1 minus cos squared theta right parenthesis plus left parenthesis 2 minus 4 cos squared theta plus 2 cos to the power of 4 theta right parenthesis plus left parenthesis 1 minus 3 cos squared theta plus 3 cos to the power of 4 theta minus cos to the power of 6 theta right parenthesis equals cos to the power of 4 theta 1 minus cos squared theta plus 2 minus 4 cos squared theta plus 2 cos to the power of 4 theta plus 1 minus 3 cos squared theta plus 3 cos to the power of 4 theta minus cos to the power of 6 theta equals cos to the power of 4 theta 4 minus 8 cos squared theta plus 5 cos to the power of 4 theta minus cos to the power of 6 theta equals cos to the power of 4 theta 4 minus 8 cos squared theta plus 4 cos to the power of 4 theta minus cos to the power of 6 theta equals 0 cos to the power of 6 theta minus 4 cos to the power of 4 theta plus 8 cos squared theta equals 4 end style

Answered by Rashmi Khot | 20th Sep, 2015, 01:40: PM