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ozzi
1 year ago
13

Solve: 2 + = 2. Give solutions in interval [0, 2)

Mathematics
1 answer:
Dovator [93]1 year ago
7 0
\because\cos 2x+\sin x=\sin 2x\because\sin 2x=2\sin xcosx\because\cos 2x=\cos ^2x-\sin ^2x

→ Substitute cos 2x and sin 2x by their expressions

\therefore\cos ^2x-\sin ^2+\sin x=2\sin x\cos x

→ Subtract both sides by sin x

\cos ^2x-\sin ^2x=2\sin xcosx-\sin x

→ Take sin x as a common factor in the right side

\therefore\cos ^2x-\sin ^2x=\sin x(2\cos x-1)

From the graph, the equation has 4 solutions, the intersection points between the 2 graphs

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