The value of     ​$$\frac{\sin^2{10^\circ} + \sin^2{20^\circ} + \sin^2{30^\circ} + \sin^2{40^\circ} + \sin^2{50^\circ} + \sin^2{60^\circ} + \sin^2{70^\circ} + \sin^2{80^\circ} + \sin^2{90^\circ}}{\cos^2{20^\circ} + \cos^2{40^\circ} + \cos^2{50^\circ} + \cos^2{70^\circ} + \cos^2{45^\circ}}$$ is ?

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Correct option is C

Given:  

$$\frac{\sin^2{10^\circ} + \sin^2{20^\circ} + \sin^2{30^\circ} + \sin^2{40^\circ} + \sin^2{50^\circ} + \sin^2{60^\circ} + \sin^2{70^\circ} + \sin^2{80^\circ} + \sin^2{90^\circ}}{\cos^2{20^\circ} + \cos^2{40^\circ} + \cos^2{50^\circ} + \cos^2{70^\circ} + \cos^2{45^\circ}}$$

​Identity Used:

$$\sin^2{\theta} + \sin^2{(90^\circ - \theta)} = 1$$ 

$$: \cos^2{\theta} + \cos^2{(90^\circ - \theta)} = 1$$​​​

Solution:

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