If sin 2A = cos 75°, then the smallest positive value of A is:

Correct option is A

Given:
sin 2A = cos $$75^\circ$$​​

Formula Used:

sin ($$90^\circ-\theta)$$ =cos$$\theta$$

Solution:

$$\sin 2A = \cos 75^\circ \\ \ \\ 2A = 90^\circ - 75^\circ = 15^\circ \\ \ \\A = \frac{15^\circ}{2} = 7.5^\circ$$​