If sinA +2cosA=1 prove that 2sinA-cosA=2
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Yogita Ingle 5 years, 3 months ago
Given that Sin A + 2 cos A = 1
Squaring on both sides, we get
(sin A + 2 cos A)2 = 1
We know that (a+b)2 = a2 + b2 + 2ab.
(sin2 A + 4 cos2 A + 4 sin A cos A) = 1
4 cos2 A + 4 sin A cos A = 1 - sin2 A
4 cos2 A + 4 sin A cos A = cos2 A
3 cos2 A + 4 sin A cos A = 0
3 cos2 A = - 4 sin A cos A ---- (1).
Given 2 sin A - cos A
Squaring on both sides, we get
(2 sin A - cos A)2 = 4 sin2 A + cos2 A - 4 sin A cos A
= 4 sin2 A + cos2 A + 3 cos2 A
= 4 sin2 A + 4 cos2 A
= 4(sin2 A + cos2 A)
= 4.
2 sin A - cos A = 2.
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