Question

if sinA + 2cosA=1 prove that 2sinA-cosA = 2

Answer 1

Answer:

Sin A + 2 Cos A = 1

Squaring on both sides, we get,

=> ( Sin A + 2 Cos A )² = 1²

=> Sin²A + 4 Cos²A + 4 Sin A. Cos A = 1

=> 4 Cos²A + 4 Sin A.Cos A = 1 - Sin²A

=> 4 Cos²A + 4 SinA.CosA = Cos²A

=> 4 Cos²A - Cos²A = - 4 SinA.CosA

=> 3 Cos²A = - 4 SinA.CosA    .....( 1 )

Now let us take ( 2 Sin A - Cos A )², we get,

=> ( 2 Sin A - Cos A )² = 4 Sin²A + Cos²A - 4 SinA.CosA   ....( 2 )

Now substituting ( 1 ) in ( 2 ) , we get,

=> ( 2 Sin A - Cos A )² = 4 Sin²A+ Cos²A + 3 Cos²A

=> ( 2 Sin A - Cos A )² = 4 Sin²A + 4 Cos²A

=> ( 2 Sin A - Cos A )² = 4 ( Sin²A + Cos²A )

=> ( 2 Sin A - Cos A )² = 4 ( 1 )

=> ( 2 Sin A - Cos A )² = 4

Taking Square root on both sides we get,

=> ( 2 Sin A - Cos A ) = √ 4

=> ( 2 Sin A - Cos A ) = 2

Hence proved !

Answer 2

Hey Mate ⭐⭐⭐

Here's ur answer ⤵⤵⤵

Answer=>

sinA + 2cosA=1

Squarring both sides , we get

sin 2 A + 4 cos2 A +4 sin A cos A =1

4 cos 2 A +4 sin  A. cos A = 1 - sin 2 A

4 cos 2 A + 4 sin A cos A = cos 2 A

3 cos 2 A + 4 sin A cos A =0....(i)

Now, ( 2 sin A - cos A)2= 4 sin 2 A + cos 2 A -4 sin A cos A

=4 sin 2 A + cos 2 A +3 cos 2 A

= 4 (sin 2 A + cos 2 A)

=4

Thus, 2 sin A - cos A = 2

Hope it helps you! ヅ

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