Question

If 3 sinb + 5 cosb =5 then show that 3 cosb - 5 sinb =±3

Answer 1

(3sinb+5cosb)^2 = 9sin^2b + 30sinb cosb + 25cos^2b

(3cosb-5sinb)^2 = 9cos^2b - 30sinb cosb + 25sin^2b
adding, you get
(3sinb+5cosb)^2 + (3cosb-5sinb)^2 = 9+25 = 34
5^2 + (3cosb-5sinb)^2 = 34
now finish it off