Question

if cosA+root3 sinA=2SinA.show that sinA-root3 CosA=2CosA

Answer 1

Answer:

Step-by-step explanation:

2cos A = root 3

Cos A = root 3/2

Angle A =30°

So the

2SinA + root3 tanA

2Sin30° + root3 tan30°

1 + 1

2

Answer 2

$\cos(a) + \sqrt{3} \sin(a) = 2 \sin(a) \\ = \cos(a) = 2 \sin(a) - \sqrt{3} \sin(a) \\ = \cos(a) = \sin(a) (2 - \sqrt{3} ) \\ = \sin(a) = \frac{ \cos(a) }{2 - \sqrt{3} }$

On rationalizing the denominator, we get :

$\sin(a) = \cos(a) (2 + \sqrt{3} ) - - - - - 1$

Now, to prove :

$\sin(a) - \sqrt{3} \cos(a) = 2 \cos(a )$

$lhs = \sin(a) - \sqrt{3} \cos(a)$

On substituting value of sin(a) from eq 1, we get:

$\cos(a) (2 + \sqrt{3} ) - \sqrt{3} \cos(a) \\ = 2 \cos(a) + \sqrt{3} \cos(a) - \sqrt{3} \cos(a) \\ = 2 \cos(a) = rhs$

Hence proved.

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