Final answer:
The equation 10cos^4(t) = (15/4)5cos(2t)(5/4)cos(4t) simplifies to 44cos^4(t) - 44cos^2(t) + 10 = 375cos(4t), which is a quartic equation with four possible solutions for cos(t). The correct answer is cos(t) (option A).
Step-by-step explanation:
To solve the equation 10cos^4(t) = (15/4)5cos(2t)(5/4)cos(4t), we can simplify the equation using trigonometric identities. Firstly, we can rewrite cos^4(t) as (cos^2(t))^2. Then, we can use the identity cos(2t) = 2cos^2(t) - 1 to substitute for cos(t). Doing these steps, we get:
10(2cos^2(t) - 1)^2 = (15/4)5(2cos^2(t) - 1)(5/4)cos(4t)
Expanding and simplifying the equation further, we obtain:
44cos^4(t) - 44cos^2(t) + 10 = 375cos(4t)
Now, we can solve for cos(t) in this equation. However, it is important to note that the equation is a quartic equation, which means it has four possible solutions for cos(t). Therefore, the correct answer is cos(t) (option A).