Question

value of theta will be?

Answer 1

we know that sin theta is equal to sin theta by 2 cos theta by 2
Therefore
U is equal to 2 cos theta by 2
Cos inverse u/2=theta by 2
theta equal to 2 Cos inverse u by 2

Answer 2

We will use the identity:
$\boxed{\sin \theta = 2\, \sin \frac{\theta}{2} \, \cos\frac{\theta}{2}}$


Now, we can solve as follows:

$u \times \sin \frac{\theta}{2} = \sin \theta \times 1 \\ \\ \\ \implies u \sin \frac{\theta}{2} = 2\sin \frac{\theta}{2}\cos \frac{\theta}{2} \\ \\ \\ \implies2\sin \frac{\theta}{2} \cos \frac{\theta}{2} - u \sin \frac{\theta}{2} =0 \\ \\ \\ \implies \sin \frac{\theta}{2} \left( 2\cos \frac{\theta}{2} -u \right) = 0 \\ \\ \\ \implies \sin \frac{\theta}{2} = 0 \quad OR \quad 2\cos \frac{\theta}{2} - u = 0 \\ \\ \\ \implies \frac{\theta}{2} = 0 \quad OR \quad \cos \frac{\theta}{2} = \frac{u}{2}$


$\implies \theta = 0 \quad OR \quad \frac{\theta}{2} = \cos^{-1} \frac{u}{2} \\ \\ \\ \impies \boxed{\theta=0} \quad OR \quad \boxed{\theta = 2\cos^{-1}\frac{u}{2}}$


Thus, the value of $\theta$ can be $0$ or $2\cos^{-1}\frac{u}{2}$