Question

The proof below shows that sin theta -sin^3 theta=sin2theta cos^2 theta/2cos theta

Answer 1

Given:

Given the steps of the proof of the equation

`\sin\theta-\sin^3\theta=(2\sin2\theta\cos^2\theta)/(2\cos\theta)`

Required: Expression missing on the thrd step

Step-by-step explanation:

The second step is

`\sin\theta-\sin^3\theta=\sin\theta(1-\sin^2\theta)(2\cos\theta)/(2\cos\theta)`

from which leads to

`\sin\theta-\sin^3\theta=((2\sin\theta\cos\theta)(1-\sin^2\theta))/(2\cos\theta)`

The expression missing on the third step is

`((2\sin\theta\cos\theta)(1-\sin^2\theta))/(2\cos\theta)`

Option D is correct.

Final Answer:

`((2\sin\theta\cos\theta)(1-\sin^2\theta))/(2\cos\theta)`