Question

If sin A+2 cos A= 1 then prove 2 sin A - cosA=2

Answer 1

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 = a^2 + b^2 + 2ab.

(sin^2 A + 4 cos^2 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    

3 cos^2 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 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 + 4 cos^2 A

                               = 4(sin^2 A + cos^2 A)

                               = 4.

2 sin A - cos A = 2.


LHS  = RHS.


Hope this helps!

Answer 2

Answer:

Step-by-step explanation:

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