d) If $$ 9 \cos A-7=0 $$, find the value of $$ \operatorname{cosec}^{2} A $$.

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Given the equation
$$
9 \cos A - 7 = 0,
$$
we first solve for $$\cos A$$:
$$
9 \cos A = 7 \quad \Rightarrow \quad \cos A = \frac{7}{9}.
$$

Next, we use the Pythagorean identity:
$$
\sin^2 A + \cos^2 A = 1.
$$
Substitute $$\cos A = \frac{7}{9}$$ into the identity:
$$
\sin^2 A = 1 - \cos^2 A = 1 - \left(\frac{7}{9}\right)^2 = 1 - \frac{49}{81} = \frac{81-49}{81} = \frac{32}{81}.
$$

The cosecant function is the reciprocal of the sine, so
$$
\operatorname{cosec}^2 A = \frac{1}{\sin^2 A} = \frac{1}{\tfrac{32}{81}} = \frac{81}{32}.
$$
$$ \operatorname{cosec}^{2} A = \frac{81}{32} $$

d) If , find the value of .

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