Question

1-cos(12x)=____.
A. 2cos^2(12x)
B. 2cos^2(6x)
C. 2sin^2(12x)
D. 2sin ^2(6x)

Answer 1

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

How to simplify a trigonometric equation

Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:

1. 1 - cos 12x      Given
2. 1 - cos² 6x + sin² 6x         cos 2x = cos² x - sin² x / (- 1) · a = - a
3. 1 - 1 + sin² 6x + sin² 6x       cos² x + sin² x = 1 / (- 1) · a = - a
4. 2 · sin² 6x     Definitions of subtraction and addition / Existence of additive inverse / Modulative property / Result

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

To learn more on trigonometric equations: https://brainly.com/question/23599274

#SPJ1