5. $2\sin^2\theta - 1 = 1 - 2\cos^2\theta$ 6. $\sec\theta - \tan\theta\sin\theta = \frac{1}{\sec\theta}$ 7. $\frac{\sin\theta + \tan\theta}{1 + \sec\theta} = \sin\theta$
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Step 1: Verify the identity 2sin^(2)θ - 1 = 1 - 2cos^(2)θ Starting with the left side: 2sin^(2)θ - 1 = 2(sinθ)^2 - 1 = 2(1 - cos^(2)θ) - 1 = 2 - 2cos^(2)θ - 1 = 1 - 2cos^(2)θ Therefore, the identity 2sin^(2)θ - 1 = 1 - 2cos^(2)θ is verified. Show more…
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