3.4.7 Trigonometry (A-level only)

Prove that:

a.

$sin⁡4α−cos⁡4α≡1−2cos⁡2α\sin^4 \alpha - \cos^4 \alpha \equiv 1 - 2\cos^2 \alpha$

[2]

b.

Hence solve, for $\leq \alpha \leq 360$ , the equation,

\sin^4 \alpha - \cos^4 \alpha = 0.5

[4]

Prove that:

a.

$sin⁡4α−cos⁡4α≡1−2cos⁡2α\sin^4 \alpha - \cos^4 \alpha \equiv 1 - 2\cos^2 \alpha$

[2]

b.

Hence solve, for $\leq \alpha \leq 360$ , the equation,

\sin^4 \alpha - \cos^4 \alpha = 0.5

[4]

3.4.7 Trigonometry (A-level only) Questions