Mathematics - Trigonometric Equation Question with Solution | TestHub

The given condition can be written as:

$${\left({\cos }^2\alpha +{\sin }^2\alpha \right)}^3-3{\sin }^2\alpha {\cos }^2\alpha \left({\cos }^2\alpha +{\sin }^2\alpha \right)+k{\sin }^{2}2\alpha =1$$

This simplifies to:

$$\left(-\frac{3}{4}\right){\sin }^{2}2\alpha +k{\sin }^{2}2\alpha =0$$

From this, we can deduce that $k=\frac{3}{4}$.