Question

if sina + 2cosa = 1
then prove
2sina - cosa = 2

Answer 1

hello hope this helps you

Answer 2

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.