Home > Trigonometry > Double Angle Identities

How do you use the double-angle formula to rewrite the expression: #(1/3)cos^2x-(1/6)#?

Answer 1

Charles Autterson

Use the trig identity: #cos 2a = 2. cos^2 (a) - 1#.

#y = 1/3. cos^2 (x/3) - (1/6) = 1/6. (2cos^2 (x/3) - 1) = 1/6 cos ((2x)/3)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Brooklyn Anderson

To rewrite the expression (1/3)cos^2(x) - (1/6) using the double-angle formula, follow these steps:

Recognize that cos(2x) = 2cos^2(x) - 1.
Rearrange the formula to solve for cos^2(x):

cos^2(x) = (1/2)(cos(2x) + 1).
Substitute the expression for cos^2(x) into the original expression:

(1/3)[(1/2)(cos(2x) + 1)] - (1/6).
Simplify the expression:

(1/6)cos(2x) + (1/6) - (1/6).
Combine like terms:

(1/6)cos(2x).

Thus, the expression (1/3)cos^2(x) - (1/6) can be rewritten as (1/6)cos(2x).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided 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.