Given that cos(3x)=acos^x−bcosx is a trigonometric identity, what is the value of a+b ?
To find the value of a + b in the given trigonometric identity, cos(3x) = acos^x - bcosx, we can compare the corresponding coefficients of the terms on both sides of the equation.
Let's start by manipulating the given equation to an equivalent form that will help us compare coefficients. Using the double angle formula, we can express cos(3x) as follows:
cos(3x) = 4cos^3(x) - 3cos(x)
Now, if we compare this with the given equation, we can see that the coefficient of cos^3(x) on the left side is 4, and on the right side, it is a.
Therefore, we can conclude that a = 4.
Similarly, the coefficient of cos(x) on the left side is -3, and on the right side, it is -b.
Thus, b = 3.
Finally, to find the value of a + b, we just add the values of a and b:
a + b = 4 + 3 = 7
Therefore, the value of a + b is 7.