Final Answer
Step-by-step Solution
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Apply the trigonometric identity: $\sin\left(\theta \right)$$=\frac{\sqrt{\sec\left(\theta \right)^2-1}}{\sec\left(\theta \right)}$, where $x=2\theta$
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$\frac{1}{4}\left(\frac{\sqrt{\sec\left(2\theta\right)^2-1}}{\sec\left(2\theta\right)}\right)^2$
Learn how to solve problems step by step online. Simplify the trigonometric expression 1/4sin(2t)^2. Apply the trigonometric identity: \sin\left(\theta \right)=\frac{\sqrt{\sec\left(\theta \right)^2-1}}{\sec\left(\theta \right)}, where x=2\theta. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Simplify \left(\sqrt{\sec\left(2\theta\right)^2-1}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals 2. Multiply \frac{1}{2} times 2.