Question

the value of 2 cos 2 30 degrees-1 degree​

Answer 1

Answer:

Hope it helps you.

Step-by-step explanation:

The value of cos^2(30) is 3/4.

Solution- Since the value of cos(30) from the trigonometric values table is ✓3/2.

So if Cos(30)= ✓3/2

Then, cos^2(30)= (✓3/2)^2 = 3/4

Answer 2

Answer: The value of 2cos²(30°) - 1  is equal to 0.5

Step-by-step explanation:

cos(2θ) = cos²θ - sin²θ

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 + cos²θ

cos(2θ) = 2cos²θ - 1

Comparing the RHS of the equation with given sum in question,

2cos²(30°) - 1  =  2cos²θ - 1

⇒ θ  = 30°

∴ 2cos²(30°) - 1 = cos(2(30°))

⇒ 2cos²(30°) - 1 = cos(60°)

⇒ 2cos²(30°) - 1  =  1/2

⇒ 2cos²(30°) - 1  =  0.5

Alternate method :

cos(30°) = $\frac{\sqrt{3} }{2}$

Substituting the value of cos(30°) in given sum :

2cos²(30°) - 1

⇒ $2(\frac{\sqrt{3} }{2} )^{2} -1$

⇒ $2(\frac{3}{4}) -1$

⇒ $\frac{3}{2} -1$

⇒ $\frac{1}{2}$

⇒ 0.5

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