How do you solve #cos 2x =  sqrt3 / 2# using the double angle identity?
Solve:
Ans:
By signing up, you agree to our Terms of Service and Privacy Policy
To solve ( \cos(2x) = \frac{\sqrt{3}}{2} ) using the double angle identity, follow these steps:

Use the double angle identity ( \cos(2x) = 2\cos^2(x)  1 ).

Substitute ( \cos(2x) ) with ( 2\cos^2(x)  1 ) in the equation: [ 2\cos^2(x)  1 = \frac{\sqrt{3}}{2} ]

Add 1 to both sides of the equation: [ 2\cos^2(x) = 1  \frac{\sqrt{3}}{2} ]

Simplify the right side: [ 2\cos^2(x) = \frac{2  \sqrt{3}}{2} ]

Divide by 2: [ \cos^2(x) = \frac{2  \sqrt{3}}{4} ]

Take the square root of both sides: [ \cos(x) = \pm \sqrt{\frac{2  \sqrt{3}}{4}} ]

Simplify the square root: [ \cos(x) = \pm \frac{\sqrt{2  \sqrt{3}}}{2} ]

Since ( \cos(x) = \frac{\sqrt{3}}{2} ) lies in the third and fourth quadrants (where cosine is negative), the solution is: [ x = \pm \frac{5\pi}{6} + 2n\pi ] [ x = \pm \frac{7\pi}{6} + 2n\pi ] where ( n ) is an integer.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you solve #sin(x) = cos(x)#?
 How to use fundamental identities to simplify 9sinβtanβ+9cosβ ?
 How do you use the half angle formulas to determine the exact values of sine, cosine, and tangent of the angle #pi/8#?
 How do you solve #1  2(sinx)^2 = cosx, 0 <= x <= 360#. Solve for #x#?
 How do you verify the identity #1/(1sintheta)+1/(1+sintheta)=2sec^2theta#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7