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Question

# Write the letter of the correct answer. If$\sin \theta = \frac { 2 } { 3 }$, then$\cos 2 \theta =$__.

Solution

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Step 1
1 of 3

Given in problem : $\sin\theta=\dfrac{2}{3}$

To find the value of $\cos 2\theta$ we will use formula $\cos2\theta=\cos^2\theta-\sin^2\theta$ so we need first find the value of $\cos^2 theta$. So we have :

\begin{align*} \cos^2 \theta&=1-\sin^2\theta &&\text{\color{#4257b2}Pythagorean identity \sin^2x+\cos^2x=1}\\ \\ &=1-\left(\dfrac{2}{3}\right)^2&&\text{\color{#4257b2}Putting the value}\\ \\ &=\dfrac{9-4}{9} &&\text{\color{#4257b2}Taking LCM}\\ \\ &=\dfrac{5}{9} &&\text{\color{#4257b2}Simplifying} \end{align*}

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