SOLUTION: Dear Sir/Madam, Please help me solve this problem: Show that (1-sinA+cosA)^2 = 2(1-sinA)(1+cosA) Thank you for your help Sir/Madam.

Algebra ->  Trigonometry-basics -> SOLUTION: Dear Sir/Madam, Please help me solve this problem: Show that (1-sinA+cosA)^2 = 2(1-sinA)(1+cosA) Thank you for your help Sir/Madam.      Log On


   

Question 914353: Dear Sir/Madam,
Please help me solve this problem:
Show that (1-sinA+cosA)^2 = 2(1-sinA)(1+cosA)
Thank you for your help Sir/Madam.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
L.H.S. = %281-sinA+%2B+cosA%29%5E2+
= 1+%2B+sin%5E2%28A%29+%2B+cos%5E2%28A%29-2sin%28A%29%2B+2cos%28A%29+-2+sin%28A%29cos%28A%29
=+1%2B+1+-+2+sin%28A%29+%2B+2+cos%28A%29+-+2+sin%28A%29+cos%28A%29

=+2+-+2+sin%28A%29%2B+2cos%28A%29+-+2sin%28A%29+cos%28A%29
=2+%28+1%28+1-+sin%28A%29%29+%2B+cos%28A%29%28+1-+sin%28A%29%29%29

= 2+%28+1-+sin%28A%29+%29+%28+1+%2B+cos%28A%29%29 = R.H.S.