What is the general solution of \cos^{100}x-\sin^{100}x=1?
- A. n\pi ✓
- B. (2n+1)\pi
- C. 2n\pi
- D. (2n+1)\pi/2
Correct Answer: A. n\pi
Explanation
We can rewrite the equation as \cos^{100}x = 1 + \sin^{100}x. Since the maximum value of \cos^{100}x is 1 and the minimum value of \sin^{100}x is 0, equality can hold <strong>ONLY</strong> when \cos^{100}x = 1 and \sin^{100}x = 0. This occurs when \cos x = \pm 1, which corresponds to x = n\pi, where n is an integer.