Question

cos²A + cos² (60° + A) + cos² (60° - A)=3/2​

Answer 1

I think there should be a cos²A in right hand side. Then it will be full filled. I hope it will help you.

Answer 2

Therefore the given trigonometric function cos²A + cos² (60° + A) + cos² (60° - A)=3/2​ is true for every value of 'A'.

Given:

The trigonometric equation: cos²A + cos² (60° + A) + cos² (60° - A)=3/2​

To Find:

The value of 'A'.

Solution:

The given question can be solved very easily as shown below.

Given trigonometric function: cos²A + cos² (60° + A) + cos² (60° - A)=3/2​

We know that, cos² x = ( 1 + cos 2x )/2

⇒ ( 1 + cos 2A )/2 + ( 1 + cos 2 (60 + A )/2 ) + ( 1 + cos 2(60 - A)/2 ) = 3/2

⇒ ( 1 + cos 2A) + ( 1 + cos(120 + 2A ) ) + ( 1 + cos (120 - 2A ) = 3

→ We know that Cos ( x + y ) = cos x. cos y - sin x. siny

→ And also cos ( x - y ) = cos x. cos y + sin x. sin y

⇒ Now, 3 + cos 2A + cos 120. cos 2A - sin 120. sin 2A + cos 120. cos 2A + sin 120. sin 2A = 3

⇒ cos 2A + 2. cos 120. cos 2A = 0

⇒ cos 2A [ 1 + 2cos 120 ] = 0

⇒ cos 2A [ 1 + 2 ( -1/2 ) ] = 0

⇒ cos 2A × 0 = 0

So the relation holds for every value of 'A'.

Therefore the given trigonometric function cos²A + cos² (60° + A) + cos² (60° - A)=3/2​ is true for every value of 'A'.

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