If sin x + cos x = a then sin^6 x + cos^6 x =
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Square the given equation.
We are given $\sin x + \cos x = a$.
Squaring both sides:
$$(\sin x + \cos x)^2 = a^2$$
$$\sin^2 x + \cos^2 x + 2 \sin x \cos x = a^2$$
Using the identity $\sin^2 x + \cos^2 x = 1$:
$$1 + 2 \sin x \cos x = a^2$$
$$2 \sin x \cos x = a^2 - 1$$
$$\sin x \cos x = \frac{a^2 - 1}{2}$$
Step 2: Express $\sin^6 x + \cos^6 x
