Which of the following completes the above identity? Which of the following comp

Question

Which of the following completes the above identity?

Which of the following completes the above identity?

sin (2x)cos(2x) To the right, half of an identity and the graph of this half are given. Use the graph to make a conjecture as to what the right side of the identity should be. Then prove your conjecture. The viewing window is [-2, 2. / 2] by sin x cos x Which of the following completes the above identity? O csc x O sec x sec x Which of the following proves the conjectured identity? Ocos x sin x- sin3 x O sin x cos2 x+ sin 3x sin x cos x Ocos3 x - sin 2 x cos x Click to select your answer

Explanation / Answer

sin 2x / sin x - cos 2x / cos x

2 sin x cos x / sin x - (cos^2 x - sin^2 x ) / cos x

= 2 cos^2 x - cos^2 x + sin^2 x / cos x

= 1 / cos x

= sec x

4th option is correct

above identity is sec x

( cos^2 x sin x + sin^3 x ) / ( cosx sin x )

proves the conjectured identity

3rd option is correct

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