The number of real numbers lambda for which t | vedclass

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Question

(b)

We have,

$\frac{\sin (\lambda, \alpha) \cos (\lambda \alpha)}{\sin \alpha \quad \cos \alpha}=\lambda-1$

$\Rightarrow \cos \alpha \sin \la

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(b)

We have,

$\frac{\sin (\lambda, \alpha) \cos (\lambda \alpha)}{\sin \alpha \quad \cos \alpha}=\lambda-1$

$\Rightarrow \cos \alpha \sin \lambda \alpha-\cos (\lambda \alpha)$

$\Rightarrow \sin (\lambda-1) \alpha=\frac{\lambda-1}{2} \sin 2 \alpha$

$	herefore \quad \lambda-1=2 	ext { or } \lambda-1=0$

$	herefore \quad \lambda=3 	ext { or } \lambda=1$

Hence, $\lambda$ has two values.

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

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