TRIGONOMETRIC EQUATIONS AND IDENTITIES

Question

Solve:  2 sin 𝑥 cos 𝑥 = 1  on the interval  0 ≤ 𝑥 < π

Answer 1

2sinxcosx = 1

sin(2x) = 1

2x = π/2 + 2kπ

x = π/4 + kπ, k = 0, 1, -1, 2, -2, ...

If k = 0, then x = π/4

All other choices for k give values of x that lie outside of the given interval.

Answer 2

2 sin x cos x = 1

2 [(1/2)(sin 2x sin 0] = 1

sin 2x sin 0 = 1

(sin 2x) (0) = 1

0 = 1

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