Question

using the formula cos 2 theta = 2 cos² theta - 1 , find the value of cos 30° , it is being given that cos 60° = 1/2​

Answer 1

Answer:

cos (30) =√3/2

Step-by-step explanation:

cos 2 theta=2 cos^2 theta -1

cos 2(30)=2 cos^2(30)-1

cos (60)=2 cos^2(30)-1

if cos 60=1/2 then

1/2=2 cos^2 (30) -1

(1/2)+1=2 cos^2 (30)

3/2=2 cos^2 (30)

3/2*2=cos^2 (30)

3/4=cos^2 (30)

√(3/4)=cos (30)

√3/2=cos (30)

Answer 2

Answer:

cos30° = √3/2

Step-by-step explanation:

Given ,

cos60° = 1/2

cos2θ = 2cos²θ - 1

To Find :-

Value of 'cos30°'

How To Do :-

We need to find the value of 'cos30°' by substituting 30° in place of 'θ' in the given formula and after simplifying we need to substitute the value of cos60° in that formula and we need to find the value of 'cos30°'.

Formula Required :-

1) cos2θ = 2cos²θ - 1

2)  cos²x = (cosx)²

$\bold{\cal{SOLUTION}}$

Substituting '30°' in place of 'θ' in the above equation :-

cos2(30°) = 2cos²(30°) - 1

cos60° = 2cos²30° - 1

1/2 = 2cos²30° - 1

[ ∴ cos60° = 1/2 ]

1/2 + 1 = 2cos²30°

(1 + 2)/2 = 2cos²30°

3/2 = 2cos²30°

3/(2 × 2) = cos²30°

3/4 = cos²30°

3/4 = (cos30°)²

[ ∴ cos²x = (cosx)² ]

$\sqrt{\dfrac{3}{4}}=cos30^{\circ}$

√3/√4 = cos30°

√3/2 = cos30°

∴ cos30° = √3/2