If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$ and $$\frac{{

Question

If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$ and $$\frac{{{\text{sin }}\alpha }}{{{\text{sin }}\beta }} = b{\text{,}}$$ then the value of $${\sin ^2}\beta $$ in terms of a and b is?

Options:

A . $$\frac{{{a^2} + 1}}{{{a^2} - {b^2}}}$$

B . $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$

C . $$\frac{{{a^2} - 1}}{{{a^2} - {b^2}}}$$

D . $$\frac{{{a^2} - 1}}{{{a^2} + {b^2}}}$$

Answer: Option C

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