If $$117 \cos^2 A + 129 \sin^2 A = 120$$ and $$170 \cos^2 B + 158 \sin^2 B = 161$$, then the value of $$\cosec^2A \sec^2B$$ is:

$$117 \cos^2 A + 129 \sin^2 A = 120$$

$$=$$>  $$117\cos^2A+117\sin^2A+12\sin^2A=120$$

$$=$$>  $$117\left(\cos^2A+\sin^2A\right)+12\sin^2A=120$$

$$=$$>  $$117\left(1\right)+12\sin^2A=120$$

$$=$$>  $$12\sin^2A=3$$

$$=$$>  $$\sin^2A=\frac{3}{12}$$

$$=$$>  $$\operatorname{cosec}^2A=\frac{12}{3}$$

$$=$$>  $$\operatorname{cosec}^2A=4$$

$$170 \cos^2 B + 158 \sin^2 B = 161$$

$$=$$>  $$12\cos^2B+158\cos^2B+158\sin^2B=161$$

$$=$$>  $$12\cos^2B+158\left(\cos^2B+\sin^2B\right)=161$$

$$=$$>  $$12\cos^2B+158\left(1\right)=161$$

$$=$$>  $$12\cos^2B=3$$

$$=$$>  $$\cos^2B=\frac{3}{12}$$

$$=$$>  $$\sec^2B=\frac{12}{3}$$

$$=$$>  $$\sec^2B=4$$

$$\therefore\ $$ $$\cosec^2A \sec^2B$$ = $$4\times4=16$$

Hence, the correct answer is Option B