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f(x)=cos(x)^2+1/2sin(2x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

cos2x=12sin2xcos^2x=\frac{1}{2}sin2x

Step-by-step Solution

Learn how to solve problems step by step online. Solve the trigonometric equation cos(x)^2=1/2sin(2x). Multiplying the fraction by \sin\left(2x\right). Multiply both sides of the equation by 2. Grouping all terms to the left side of the equation. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right).
Solve the trigonometric equation cos(x)^2=1/2sin(2x)

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Final answer to the exercise

x=12π+2πn, x=32π+2πn, x=0 ,  n∈Zx=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=0\:,\:\:n\in\Z

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cos2x=12 sin2x
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