Question

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

Answer 1

$\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