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solniwko [45]
2 years ago
5

HELP ON THIS PROBLEM!! Solve the following 0deg< x< 360deg: cos x= cos 2x

Mathematics
1 answer:
blsea [12.9K]2 years ago
7 0

Answer:

x=0^\circ,120^\circ,240^\circ,360^\circ

Step-by-step explanation:

<u>Use identities to set the equation up as a quadratic</u>

\cos x=\cos 2x;\:0^\circ \leq x \leq 360^\circ\\\\\cos x=2\cos^2 x-1\\\\0=2\cos^2 x-\cos x-1

<u>Make the substitution u=cos(x) and solve the quadratic</u>

<u />0=2u^2-u-1\\\\0=(2u+1)(u-1)

\displaystyle 0=2u+1\\\\0=2\cos x+1\\\\-1=2\cos x\\\\-\frac{1}{2}=\cos x\\\\120^\circ,240^\circ=x

0=u-1\\\\0=\cos x-1\\\\1=\cos x\\\\0^\circ,360^\circ=x

Hence, x=0^\circ,120^\circ,240^\circ,360^\circ

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