If sin x + cos x = a then sin6 x + cos6 x =

March 26, 2026Mathematics

ScanSolve AI Answer

March 26, 2026

Answer

a$.

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

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Square the given equation. We are given x + x = a.

Asked on March 26, 2026Mathematics

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 AnswerAnswered on March 26, 2026

Step 1: Square the given equation. We are given x + x = a. Squaring both sides: ( x + x)^2 = a^2 ^2 x + ^2 x + 2 x x = a^2 Using the identity ^2 x + ^2 x = 1: 1 + 2 x x = a^2 2 x x = a^2 - 1 x x = (a^2 - 1)/(2) Step 2: Express $^6 x + ^6 x