Question

prove the following equalities
1) 2cos2 30° -1 = 1-2 sin2 30° =cos 60°

​

Answer 1

Step-by-step explanation:

we know that

$\cos {30}^{o} = \frac{ \sqrt{3} }{2} \\ \sin {30}^{o} = \frac{1}{2} \\ \cos {60}^{o} = \frac{1}{2}$

Now to prove this we will apply the above values,

$2 \cos^{2} {30}^{o} - 1 = 1 - 2 \sin^{2} {30}^{o} = \cos{60}^{o} \\ 2 {( \frac{ \sqrt{3} }{2} })^{2} - 1 = 1 - 2 ({ \frac{1}{2} })^{2} = \frac{1}{2} \\ 2 \times \frac{3}{4} - 1 = 1 - 2 \times \frac{1}{4} = \frac{1}{2} \\ = \frac{3}{2} - 1 = 1 - \frac{1}{2} = \frac{1}{2} \\ \frac{3 - 2}{2} = \frac{2 - 1}{2} = \frac{1}{2} \\ \frac{1}{2} = \frac{1}{2} = \frac{1}{2}$

hence proved.

hope it helps.

Answer 2

Answer:-  1/2=1/2=1/2

From the trigonometric  concept we know the value of degree  :-

∴cos 30° =√3/2 ∴ sin 30°=1/2 ∴cos60°=1/2

∴Now according to the question.

Given that,  2cos2 30° -1 = 1-2 sin2 30° =cos 60°

Solution:- Now we should prove the above  equation

                from putting the above value in the equation..

            2(√3/2)²-1 = 1-2(1/2)²=1/2

             2x3/4-1=1-2x1/4=1/2

             3/2-1=1-1/2=1/2

             3-2/2=2-1/2=1/2

             1/2=1/2=1/2 ( proved) .