if sinA +2cosA = 1 prove that 2 sinA - cosA = 2
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Step-by-step explanation:
sinA+2cosA=1
squarring both sides we find
sin²A+4cos²A+4sinAcosA=1
4cos²A+4sinAcosA=1-sin²A
4cos²A+4sinAcosA=cos²A
3cos²A+4sinAcosA=0....(i)
now
(2sinA-cosA)²= 4sin²A+cos²A-4sinAcosA
=4sin²A+cos²A+ 3cos²A. ......by eq (i)
=4sin²A+4cos²A
=4(sin²A+cos²A)
=4(1)
(2sinA-cosA)²= 4
then
2sinA-cosA = 2
hence proof .....
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