Question

2cosA = √2+√2(1+cos4A)​

Answer 1

Answer:

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Answer 2

Solution :-

We Know :-

• Cos(2x) = 2 Cos²(x) - 1

Now :-

$\sf{= \sqrt{2 + \sqrt{2 ( 1 + \cos \: 4A)}}}$

$\sf{ = \sqrt{2 + \sqrt{ 2 ( 1 + 2cos^2 (2A) - 1)}}}$

$\sf{ = \sqrt{2 + \sqrt{2(2cos^2(2A))}}}$

$\sf{ = \sqrt{2 + \sqrt{4cos^2(2A))}}}$

$\sf{= \sqrt{2 + 2cos(2A) }}$

$\sf { = \sqrt{ 2( 1 + cos(2A))}}$

$\sf{ = \sqrt{2( 1 + 2cos^2(A) - 1)}}$

$\sf{= \sqrt{2(2cos^2(A))}}$

$\sf{ = \sqrt{4cos^2(A)}}$

$\boxed{ \sf{ = 2cos(A)}}$