Question

The number of real numbers $\lambda$ for which the equality $\frac{sin\left(\lambda \alpha \right)}{sin\alpha }-\frac{cos\left(\lambda \alpha \right)}{cos\alpha }=\lambda -1$, holds for all real $\alpha$ which are not integral multiples of $\frac{\pi }{2}$ is

• A. 1
• B. 2
• C. 3
• D. Infinite

Answer 1

The correct option is B 2

$\frac{sin\left(\lambda \alpha \right)}{sin\alpha }-\frac{cos\left(\lambda \alpha \right)}{cos\alpha }=\lambda -1sin\lambda \alpha cos\alpha -cos\lambda \alpha sin\alpha =(\lambda -1)sin\alpha cos\alpha sin(\lambda \alpha -\alpha )=\frac{(\lambda -1)}{2}sin2\alpha So,\lambda =1,3$