If sin theta+sin^3theta=1-sin^2theta
Prove cos^6theta-4cos^4theta+8cos^2theta=4

Asked by vans75a | 26th Sep, 2015, 12:31: PM

Expert Answer:

G i v e n space t h a t space sin theta plus sin cubed theta equals 1 minus sin squared theta rightwards double arrow s i n theta open parentheses 1 plus sin squared theta close parentheses equals 1 minus s i n squared theta rightwards double arrow s i n theta open parentheses 1 plus 1 minus cos squared theta close parentheses equals c o s squared theta rightwards double arrow s i n theta open parentheses 2 minus c o s squared theta close parentheses equals c o s squared theta S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma s i n squared theta open parentheses 2 minus c o s squared theta close parentheses squared equals c o s to the power of 4 theta rightwards double arrow open parentheses 1 minus c o s squared theta close parentheses open parentheses 2 minus c o s squared theta close parentheses squared equals c o s to the power of 4 theta rightwards double arrow open parentheses 1 minus c o s squared theta close parentheses open parentheses 4 minus 4 c o s squared theta plus cos to the power of 4 theta close parentheses equals c o s to the power of 4 theta rightwards double arrow 4 minus 4 c o s squared theta plus c o s to the power of 4 theta minus 4 c o s squared theta plus 4 c o s to the power of 4 theta minus c o s to the power of 6 theta equals c o s to the power of 4 theta rightwards double arrow negative 4 plus 4 c o s squared theta minus c o s to the power of 4 theta plus 4 c o s squared theta minus 4 c o s to the power of 4 theta plus c o s to the power of 6 theta plus c o s to the power of 4 theta equals 0 rightwards double arrow c o s to the power of 6 theta minus 4 c o s to the power of 4 theta plus 8 c o s squared theta equals 4

Answered by Vimala Ramamurthy | 26th Sep, 2015, 04:52: PM