Find the value of

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1747841775/aptidude_questions/teidtw7xtanz1cdhtvzi.png)

Question

Find the value of

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1747841775/aptidude_questions/teidtw7xtanz1cdhtvzi.png)

Accepted Answer

Step 1: Simplify numerator and denominator inside the cube.

Numerator: $sintheta - 2sin^3 theta) = sintheta (1 - 2sin^2 Theta)

Denominator: \(2cos^3 theta - cos theta) = cos theta (2cos^2 theta - 1)

Step 2: Recall the double angle identities:
\(cos 2theta = 1 - 2sin^2 theta) and \(cos 2theta = 2cos^2 theta - 1)

Similarly, simplifying using identities.

Therefore, the value of the expression is \(-1$.

Answer

Answer

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