Question 43

What is the simplified value of $$\ \frac{2sin^{3}\ \theta\ - sin\theta}{cos\theta\ -\ 2\ cos^{3}\ \theta}$$?

Solution

Expression : $$\ \frac{2sin^{3}\ \theta\ - sin\theta}{cos\theta\ -\ 2\ cos^{3}\ \theta}$$

= $$\ \frac{sin\ \theta(2sin^{2}\ \theta\ - 1)}{cos\ \theta(2 -\ 2\ cos^{2}\ \theta)}$$

= $$\frac{sin\ \theta(cos2\ \theta)}{cos\ \theta(cos2\ \theta)}$$

= $$\frac{sin\ \theta}{cos\ \theta}=tan\ \theta$$

=> Ans - (A)

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