Prove that sin^2A+2cos^2A+3son^2A+4cos^2A+.....+89sin^2A+90cos^2A=2085

Asked by nitinkumarsingh.singh.75 | 23rd Nov, 2015, 06:20: PM

Expert Answer:

sin squared A plus 2 cos squared A plus 3 sin squared A plus 4 cos squared A plus.... plus 89 sin squared A plus 90 cos squared A equals open parentheses s i n squared A plus 3 s i n squared A plus... plus 89 s i n squared A close parentheses plus open parentheses 2 c o s squared A plus 4 c o s squared A plus... plus 90 c o s squared A close parentheses equals sin squared A open parentheses 1 plus 3 plus 5 plus... plus 89 close parentheses plus cos squared A open parentheses 2 plus 4 plus... plus 90 close parentheses equals sin squared A cross times 45 over 2 open parentheses 1 plus 89 close parentheses plus c o s squared A cross times 45 over 2 open parentheses 2 plus 90 close parentheses equals 2025 sin squared A plus 2070 cos squared A equals 2025 s i n squared A plus 2025 c o s squared A plus 45 cos squared A equals 2025 open parentheses sin squared A plus cos squared A close parentheses plus 45 c o s squared A equals 2025 plus 45 c o s squared A  P. S. space T h e space a n s w e r space i s space n o t space m a t c h i n g space w i t h space t h e space r i g h t space h a n d space s i d e space o f space t h e space q u e s t i o n. space P l e a s e space c h e c k space t h e space q u e s t i o n.

Answered by satyajit samal | 24th Nov, 2015, 11:42: AM